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Syllabus

The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.

^{2 }: n^{2.}show that the ratio of the m^{th}and n^{th}terms is (2m-1) : (2n-1)^{2}/2 + 5n/2, find its 25^{th }term.of the other is 7. − Find the difference between their 4th terms.

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.If the m

^{th}term of an A.P. be 1/n and n^{th}term be 1/m, then show that its (mn)^{th}term is 1.(experts please give the answers with same numbers which is provided in question don’t change the numbers and don’t provide any link.)IF THE SUM OF FIRST m TERMS OF AN AP IS n. AND THE SUM OF FIRST n TERMS IS m, THEN SHOW THAT THE SUM OF ITS FIRST( m+n) TERMS IS -(m+n).

How many 3 digit numbers are such that when divided by 7, leave a remainder 3 in each case.

Maths Project :make designs using arithmetic progression

Which term of the sequence 7.3, 6.9, 6.5, 6.1, .... is the first negative term?

if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)

the sum of the first n terms of an AP is given by s

_{n}=3n^{2}-n , determine the AP and its 25^{th}term.how to find 10term

If m times the mth term of an A.P is equal to n times its nth term, show that the (m+n)th term of the A.P is zero.

Which term of the AP is 6,19,32,45..........will be 143 more than its 34th term.the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term

The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of the first sixteen terms of the A.P. .

If pth , qth and rth term of an AP are a,b,c respectively , then show that

(a-b)r +(b-c)p + (c-a)q = 0

Please help me with this question asap .

150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d 2nd day, 4 more workers droped the 3rd day n so on..... it takes 8 more days to finish the work now ..find d no. of days in vch the work waz completed....

_{n}/s_{m}=n^{4}/m^{4}(where S_{k}is the sum of first k terms an AP a1,a2,.....)then the value of (a_{m}+1)/(a_{n}+1) in terms of m and n will bea) [(2m+1)/(2n+1)]

^{3}b) [(2n+1)/(2m+1)]^{3}c)[(2m-1)/(2n+1)]^{3 }d) [(2m+1)/(2n-1)]^{3 }, Sir , Please explain the answer.An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

_{1,}a_{2},y and x,b_{1,}b_{2},y are in A.P then a_{2}-a_{1}/b_{2-}b_{1 }is equal to ............If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289.Find the sum of first n terms

a circle with area A1 is contained in the interior of a larger circle with area A1 +A2. if the radius of the larger circle is 3units and A1,A2,A1+A2 are in A.P. , then the radius of the smaller circle is ---?

The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?

plzz reply with solution

The sum of n terms of two AP are in the ratio (2n+3):(6n+5),then the ratio of their 13th terms is

(a) 53:155

(b)29:83

(c) 31:89

(d)27:8

Please answer with complete steps and explanation.

if the sum of first m terms of an AP is am

^{2}+bm,find its common differance?the ratio of the sum of n terms of two AP's is (7n+1):(4n+27).find the ratio of their m th terms.

Answer: let a1 , a2 be the 1st terms and d1 , d2 the common differences of the two given A.P's. then the sums of their n terms are given by

Sn = n/2 {2.a1+(n-1)d1} and Sn' = n/2{2. a2 +(n-1)d2}

Sn/Sn' = n/2{2.a1+(n-1)d1} / n/2{2.a2 + (n-1)d2}

Sn / Sn' = 2.a1+(n-1)d1 / 2.a2 + (n-1)d2

it is given that

Sn / Sn' = 7n+1 / 4n + 27

2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7n+1 / 4n+27 ........................ (i)

To find the ratio of the mth terms of the two given AP's , we replace n by (2m-1) in equation (i)

therefore, 2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7(2m-1) + 1 / 4(2m-1) + 27

a1 + (m-1)d1 / a2 + (m-1)d2 = 14m - 6 / 8m + 23

Hence, the ratio of the mth terms of the two A.P's is (14m - 6) : (8m + 23)

My question is, why it has been assumed (2m-1) in the place of 'n' ? has it been arrived from solving with the help of a formula or is it a mere assumption? if it is simply an assumption, why it should be assumed as (2m-1) ? why not 2m or (m - 1)

^{th}means in the two cases are same then ratio a: b is equal to:-

(1) n : (n – m + 1) (2) (n – m + 1) : m (3) (n – m + 1) : n (4) m : (n – m + 1)

If s

_{n}, the sum of first n terms of an AP is given by s_{n}= (3n^{2}-4n), then find its nth term.How many terms of the AP , 4,7,10…….. must be taken so that the sum may be 650.

If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.

what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible

-5,-5/2,0,5/2.....

if the nth term of an AP is (2n+1) find the sum of first n terms of the AP

sum of first p , q and r terms of an A.P. are a , b and c respectively. Prove that :

a/p (q-r) + b/p(r-p) + c/r (p-q) = 0

If S

_{1}, S_{2}, S_{3}are the sum of n terms of three AP's the first term of each being unity and respective common diffrence being 1 , 2 , 3_ _ _ _ _. Prove that S_{1}+S_{3}= 2S2.which term of an AP 3,15,27,39............ will 132 more than its 54

^{th}termin an AP the first term is 22,n

^{th}term is -11 and sum of the first n terms is 66. find n and d.Divide 56 into 4 parts which are in AP such that hte ratio of product of extremes to the product of mean is 5 : 6? Hoping for a quick response......plz.....[ May be within Sunday ]

find x so that 2x+1, x

^{2}+x+1&3x^{2}- 3x+ 3 are the consecutive terms of an A.P.if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.solve the solution 1+4+7+10.............+x = 287

is

(a) -955

(b) -945

(c) -950

(d) -965

In an AP,the sum of first n term is 3n2/2+13n/2

find its 25th term

find the 6th term from the end of the AP 5,2, -1 , -4................. -31 .

if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).

Find the sum to n terms of the series 1/( 1 + 1^2 + 1^4) + 2/( 1 + 2^2 + 2^4) + 3/( 1 + 3^2 + 3^4) +......

urgent

the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.

Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.

Find the LCM of (x + 3)(6x

^{2}+ 5x+ 4) and (2x^{2}+ 7x + 3) (x + 3)(2x + 1) (x + 3) (3x + 4)

(4x

^{2}– 1) (x + 3)^{2}(3x + 4)(4x

^{2}– 1) (x + 3) (3x + 4)(2x – 1) (x – 3) (3x + 4)

Hint:30) the digits of a positive integer,having three digits are in A.P. and their sum is 15.the number obtained by reversing the digits is 594 less than the original number.find the number.

IF s

_{n }the sum of first n terms of an AP is givenby S_{n}=5n^{2}+3n then find its n^{th}termFind the sum of all the integers between 100 and 200 that are not divisible by 9

Find the sum of the series: 1+3+4+8+7+13+10+18+... to 23 terms.

In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.an A.P. consists of 60 terms.if the first and the last terms be 7 and 125 respectively,find 32nd term.

A

contractoremployed150 labourersto finish a peice of work in a certain no. of days.4 workerswent away thesecond day,4 more workerswent away thethird dayandso on. Ifit took 8 more daysto finish the work ,find the no. of days in which the work was completed.

ANURAG.Q4. Let tn be the nth term of an A.P. If $\sum _{\mathrm{r}=1}^{{10}^{99}}{\mathrm{a}}_{2\mathrm{r}}={10}^{100}\mathrm{and}\sum _{\mathrm{r}=1}^{{10}^{99}}{\mathrm{a}}_{2\mathrm{r}-1}={10}^{99}$, then the common difference A.P. is

(A) 1 (B) 10

(C) 9 (D) 10

^{99}Q5. The value of $\sum _{\mathrm{r}=1}^{\mathrm{n}}\mathrm{log}\left(\frac{{\mathrm{a}}^{\mathrm{r}}}{{\mathrm{b}}^{\mathrm{r}-1}}\right)\mathrm{is}$

$\left(\mathrm{A}\right)\frac{\mathrm{n}}{2}\mathrm{log}\left(\frac{{\mathrm{a}}^{\mathrm{n}}}{{\mathrm{b}}^{\mathrm{n}}}\right)\left(\mathrm{B}\right)\frac{\mathrm{n}}{2}\mathrm{log}\left(\frac{{\mathrm{a}}^{\mathrm{n}-1}}{{\mathrm{b}}^{\mathrm{n}}}\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right)\frac{\mathrm{n}}{2}\mathrm{log}\left(\frac{{\mathrm{a}}^{\mathrm{n}+1}}{{\mathrm{b}}^{\mathrm{n}-1}}\right)\left(\mathrm{D}\right)\frac{\mathrm{n}}{2}\mathrm{log}\left(\frac{{\mathrm{a}}^{\mathrm{n}+1}}{{\mathrm{b}}^{\mathrm{n}+1}}\right)$

Q6. If s

_{r}denotes the sum of r terms of an A.P. and $\frac{{\mathrm{s}}_{\mathrm{a}}}{{\mathrm{a}}^{2}}=\frac{{\mathrm{s}}_{\mathrm{b}}}{{\mathrm{b}}^{2}}$= c, then s_{c}is(A) c

^{3}(B) $\frac{\mathrm{c}}{\mathrm{ab}}$(C) abc (D) a + b + c

The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).

Find the sum of first five multiples of 3?

Which term of AP:121,117,113,......., is its first negative term?

A student taking test consisting of 10 quetions is told that each after the first is worth 2 mks more than the preceding ques. If 3rd ques. of the test is worh 5 mks..,what is the maximum score that the student can obtain by attempting 8 questions.

find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

help plsss

The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.

(a+b)

^{2}+ (a^{2}+b^{2}) +(a-b)^{2}+........If there are (2n+1) terms in A.P,then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n.

Find the sum of the a.p.:

(x - y)

^{2},(x^{2}+y^{2}),(x+y)^{2}...... to n terms.Find the 20th term from the last term of the AP 3, 8, 13, .....253.

1) if a , b , c are in AP , show that 1/ab , 1/ca , 1/bc are in AP .

2) if m times the mth term of an AP is equal to n times it's n term , find the (m+n)th term.

pls answer fast...

If s

_{n }denotes the sum of n terms of AP whose common difference is d and first term is a, find s_{n}-2s_{n-1}+s_{n-2}If xnotequal to y and the sequences x,a

_{1},a_{2},y and x,b_{1},b_{2,}y each are in A.P,then a_{2}-a_{1}/b_{2}-b_{1}isShow that sum of an AP whose first term is a,the second term b and the last term c,is equal to (a+c)(b+c-2a)/2(b-a)..Plzzz i need hlpp!!!!

if Sn denote the sum of n terms of an AP with first term a and common difference d such that Sx/Skx is independent of x , then-

a. d=a b. d=2a c. a =2d d. d=-a

if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.

a body falls 16 metres in the 1st second of its motion, 48 in the second, 80 in the third and so on.(i) how long will it take to fall 4096 metre? (ii) how far does it fall during the 11th second of its motion?

if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)

THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.

Q.11) If the sum of the A.P. 3, 7, 11,. is 210, the number is terms is

a 12 b 22 c 15 d 10