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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.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.a)Find the expression for number of plants in the nth row.

i) 2n + 1

ii) 2n − 1

iii) 4n − 1

iv) 2n + 3

b) Find the number of plants in the 7th row.

i) 21

ii) 7

iii) 15

iv) 17

c) If there are 25 plants in the last row, find the total number of rows.

i) 11

ii) 10

iii) 13

iv) 12

d) Assuming that Reema has kept distance between any two consecutive plants

in a row as 30 cm, find the length of the 12th row (i.e. the distance between

the first and the last plant in the 12th row neglecting the width of the plants).

i) 7.5 metres

ii) 7.2 metres

iii) 6.9 metres

iv) 7.0 metres

e) Reema’s father gifts her 50 more plants. She continues to arrange these

plants in Arithmetic Progression. She observes that she is falling short of

some plants to complete the A.P. How many minimum number of plants

does she require more to complete the A.P. ? (Assuming 25 plants in the last

row before her father gifts her 50 plants).

i) 6

ii) 7

iii) 8

iv) 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).

1. What is minimum number of days he need to practice till his goal is accomplished?

2. Write the AP for the above situation.

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)

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

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.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.

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 12th term from the end in the AP 9,5,1.....is -107.Find the last 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....

Find the sum of all the numbers less than 1000, which are neither divisible by 5 nor by 2.

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

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)

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.terms is 50. Find the A.P.

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 factory produced 1100 cars in the third year and 2700 cars in the 11th year assuming that the production increases by a fixed number every year,find the production of cars in the 20th year and total cars produced in first 20years

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

Three sets of english, hindi and maths books have to be stacked in such a way that all the books are stored topic wise and height of each stack is the same.The no. of english books is 96 , the no. of hindi books is 240 and the no. of maths books is 336. Assuming that books are of the same thickness, determine the no. of stacks of english, hindi and maths books respectively.

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 A.P. the first term is 25, nth term is -17 and the sum of first n terms is 60. 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 ]

if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.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

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).

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.

Find the sum of series 103=101+99+..............49.

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.

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

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

help plsss

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

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

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

Find the sum of first five multiples of 3?

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

HOw many terms are there in the AP : 2,9,16,...........,261

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

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

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.

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

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

the number of odd numbers between 60 and 360 is

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/

the nth term of an AP is given by a

_{n}= 4n - 5,then find the sum of first 25 terms of the AP.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 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:in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.

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.Find the common difference of an A.P in which ${a}_{16}-{a}_{12}=16$