Question

The sum of the 2^nd and 7^th terms of an AP is 30. If its 15th term is 1 less than twice its 8^th term, find AP.

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

\(\Rightarrow \) a + 14d = 2(a + 7d)-1

\(\Rightarrow \) a + 14d = 2a + 14d - 1

\(\Rightarrow \) -a = -1

\(\Rightarrow \) a = 1

Putting a = 1 in (1), we get

2 x 1 + 7d = 30

\(\Rightarrow\) 7d = 30 - 2 = 28

\(\Rightarrow\) d = 4

So,

a₂ = a + d =1 + 4 = 5

a₃ = a + 2d = 1 + 2 x 4 = 9........

Hence, the AP is 1, 5, 9, 13, …….

Answer 2

I hope it helps you.