The sum of the first 7 terms of an A.P. is 10, and that of the next 7 terms is 17. Find the progression.

Given: Sum of first 7 terms, S₇ = 10

and Sum of the next 7 terms = 17

⇒ Sum of 8^th to 14^th terms = 17

⇒ Sum of first 14 terms – Sum of first 7 terms = 17

⇒ S₁₄ – S₇ = 17

⇒ S₁₄ – 10 = 17

⇒ S₁₄ = 27

Sum of 7 terms,

⇒ 20 = 7[2a + 6d]

⇒ 20 = 14a + 42d …(i)

Sum of 14 terms,

⇒ 27 = 7[2a + 13d]

⇒ 27 = 14a + 91d …(ii)

Solving the linear equations (i) and (ii), we get

14a + 42d – 14a – 91d = 20 – 27

⇒ -49d = -7

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

20 = 14a + 42d

⇒ 20= 14a + 6

⇒ 20 – 6 = 14a

⇒ 14 = 14a

⇒ a = 1

Thus, a = 1 and

So, AP is

a₁ = 1

a₂

a₃

Hence, AP is