Question

HOW MANY term of ap 9 17 25 ....must be taken to give sum of 639.

Answer 1

bro question is wrong, i think it is 636, but any way
by taking 636 answer is

Answer 2

Let the number of the term of the A.P. be n.

Thus, Using the formula,

Sn = n/2 [2a + (n - 1)d]

where a is the first term = 9

d is the  common difference = 17 - 9 = 25 - 17 = 8

Sn = Sum  of n terms = 639

Putting these values, we get,

 639 = n/2[2× 9 + (n - 1)8]

639 × 2 = 18n + 8n(n - 1)

1278 = 8n² + 10n

∴ 8n² + 10n - 1278 = 0

∴ 4n² + 5n - 639 = 0

 (4n + 53)(n - 12) = 0

n = 12 and n = -53/4 (not possible)

Hence, the no. of terms of the A.P. is 12.

Hope it helps.