Question

The sum of the first 7 terms of an A.P. is 63 and that of its next 7 terms is 161. Find the A.P.

Answer 1

Since, `S_n = n/2 [2a + (n - 1)d]`

Given, S₇ = 63

So, `S_7 = 7/2 [2a + 6d] = 63`

⇒ 2a + 6d = 18   ...(i)

Now, sum of 14 terms is:

S₁₄ = `"S"_"first 7 terms" + "S"_"next 7 terms"`

= 63 + 161

= 224

∴ `14/2 [2a + 13d] = 224`

⇒ 2a + 13d = 32   ...(ii)

On subtracting (i) from (ii), we get

(2a + 13d) – (2a + 6d) = 32 – 18

⇒ 7d = 14

⇒ d = 2

Putting the value of d in (i), we get

a = 3

Hence, the A.P. will be: 3, 5, 7, 9, ....