Given: Sum of first 7 terms, S7 = 10
and Sum of the next 7 terms = 17
⇒ Sum of 8th to 14th terms = 17
⇒ Sum of first 14 terms – Sum of first 7 terms = 17
⇒ S14 – S7 = 17
⇒ S14 – 10 = 17
⇒ S14 = 27
⇒ 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
⇒ d = 1/7
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 d = 1/7
So, AP is
a1 = 1