Question

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

Answer 1

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

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

$\frac{a+3d}{a+16d}$ = 1 / 5.

By solving this equation,

5a +15d = a + 16d

4a = d ................ (1)

Also given sum of first 7 terms of an ap is 182.

S₇ = 182,

⇒ $\frac{7}{2}$ (2a + 6d) = 182.

By further solving this equation,

⇒ 7(a + 3d) = 182

⇒ a + 3d = 26 ....... (2)

By substitution of values from equation 1 in equation 2 we get,

⇒ a + 3(4a) = 26

⇒ 13a = 26

⇒ a = 2

Putting a in eq (1) we get

4(2) = d

d = 8.

Therefore, the AP will be 2,10,18........