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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.

Three alternate terms of an AP are x+y, x-y and 2x + 3y, then x =a) -yb) -2yc) -4yd) -6y^{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.find the 6th term from the end of the AP 5,2, -1 , -4................. -31 .

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.FIND the 4th term from the end of the A.P. ................ 2 , 5 , 8 ................ , 35If 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.Find the first positive term of the A.P: -11, -8, -5,.......

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).

the nth term of an AP is given by a

_{n}= 4n - 5,then find the sum of first 25 terms of the AP.Maths Project :make designs using arithmetic progression

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 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.

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.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 nos? plz its urgent.

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.

90.: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 first n terms of an AP whose first term is 8 and difference is 20 is equal to sum of 2n terms of another AP whose first term is -30 and common difference is 9. Find the AP

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. .

Find the middle term (s) in the A.P. 20,16,12,.........-176.

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....

the sum of the two numbers is 25 and the reciprocals is 3/10. find the numbers

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

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

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

for the finite AP 85,80,75 .......,-30 find the 5th term from the end

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)

Prove that S

_{n}, S_{2n}-S_{n}, S_{3n}-S_{2n}, S_{4n}-S_{3n}are in A.P, find out the common difference.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.find the sum of all the multiples of 7 lying between 500 and 800.

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.

a number 20 is divided into 4 parts that are in AP is 28 and sum of the first 8 terms of the same AP is 88.sum of first 16 terms of the AP is

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

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

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

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

help plsss

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.find four consecutive terms of an A.P.such that the difference of the middle term is 8 the product of the extreme terms is 217.how we are going to let the 4 consecutive terms?can we let them as a,a+d,a+2d.a+3d.i had let the terms like this but answer was not coming correct.why?

which term of an AP 3,15,27,39............ will 132 more than its 54

^{th}term14. The sequence a

_{1, }a_{2}, a_{3}, ......a_{98}satisfies the relation a_{n+1}= a_{n}+1 for n = 1, 2, 3, ...., 97 and has the sum equal to 4949, then, evaluate $\sum _{k=1}^{49}{a}_{2k}.$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 ]

if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.In an AP,the sum of first n term is 3n2/2+13n/2

find its 25th term

solve the solution 1+4+7+10.............+x = 287

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

if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.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.

whch one of the following is not an AP:

(A)13,8,3,-2,-7,-12

(B) 10.8,11.2,11.6,12,12.4

(C) 81/7,18 2/7,28 3/7,48 4/7,58 5/7

(D) 8 3/23,11 6/23,14 9/23,17 12/23

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.

let a1,a2 ,a3....,an.. . be an AP with common difference d1.And b1,b2,b3... ...bn.. .. be another AP with common difference d2.Prove that a1+b1, a2+b2 ,a3+b3,. .....+,an+bn,. ...is also an AP.Find the common difference.

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.

Find the sum of all the integers between 100 and 200 that are not divisible by 9

Q.135. If a

_{1}, a_{2}, a_{3}, .... is an arithmetic progression with common difference 1 and $\sum _{\text{i=1}}^{98}{\text{a}}_{1}\text{=137,}\phantom{\rule{0ex}{0ex}}$ then the value of a_{2}+ a_{4}+ a_{6}+ ......+ a_{98}is(1) 67

(2) 83

(3) 93

(4) 98

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.the number of odd numbers between 60 and 360 is

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.A lamp lighter has to light 100 gas lamps. He takes one and half minutes to go from one lamp post to the next. Each lamp burns 10 cubic feet of gas per hour. How many cubic feet of gas has been burnt by 8.30pm, if he lights the first/last lamp at 6pm

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?

A man repays a loan of Rs. 32500 by paying 200 in the first minth and the increased payment by Rs. 150 every month. How long will it take him to clear the loan?

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

prove that S

_{n }- S_{n-1 }= a_{n}EXPERTS,

Jobanpreet applied for a teaching job got selected. She has been offered the job with a starting monthly salary of RS. 12500 with an annual increment of RS. 1250 .Find her salary after 15 years of service .Also, find the total amount received by her in 15 years.

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

t

_{n}= n^{2}, where n is even andt

_{n}= n^{2}- 1 , where n is oddIf 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.

How many terms of the series 51, 47, 43, 39 .............. be taken to make the sum of 330?

a) 7

b) 12

c) 10

d) 15

Find the 20th term from the last term of the AP 3, 8, 13, .....253.

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

Find the sum of all two-digit numbers divisible by 2 or 3.

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.

Find the nth term and 8th term of the A.P. 1/m, 1+2m/m, 1+4m/m,...............

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

terms is 46. Find the first term of the A.P.

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.

Answer given:1050+1260-300=2010

Please explain with working.