Question

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

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.

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

By solving this equation,

5a +15d = a + 16d

4a = d ................ (i)

Also, Sum of the first 7 terms of an A.P is 182. (Given)

${\S }_7$ = 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 eq. (i) we get,

⇒ a + 3(4a) = 26

⇒ 13a = 26

⇒ a = 2

Putting a in eq (i) we get;

⇒ 4(2) = d

⇒ d = 8.

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