# The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in the ratio 1 : 5, find the AP.

Let a be the first term and d be the common difference.

Given: S7 = 182

4th and 17th terms are in the ratio 1 : 5.

i.e. [a + 3d] : [(a + 16d] = 1 : 5

=

5(a + 3 d) = (a + 16d)

5a + 15d = a + 16d

4a = d

Now, consider S7 = 182

(7/2)[2a + (7 - 1)d] = 182

(7/2)[2a + 6(4a)] = 182

7 × [26a] = 182 × 2

182a = 364

a = 2

d = 4a

d = 8

Thus the AP will be a, a + d, a + 2d,…

i.e. AP is 2, 10, 18, 26,….

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