Q29 of 202 Page 9

If the sum of 7 terms of an A.P. is 49 and that of 17 term is 289, find the sum of n terms.

S₇= 49

[2a + 6d] = 49

a + 3d = 7 (i)

S₁₇= 289

[2a + 16d] = 289

a + 8d = 17 (ii)

Subtract (i) from (ii), we get

5d = 10

d = 2

Put d = 2 in (i), we get

a = 7 – 6 = 1

S_n= [2(1) + (n – 1)2]

= n [1 + n – 1]

= n²

Find the sum of the first 25 terms of an A.P. whose n^th term is given by .

Find the sum of the first 25 terms of an A.P. whose second and third terms are 14 and 18 respectively.

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

In an A.P., the sum of first n terms is . Find its 25^th term.