The sum of first 7 terms of an AP is 10, and that of the next 7 tems is 17, find the 8th term of the AP Share with your friends Share 0 Varun.Rawat answered this Let a be the first term and d be the common difference.Sum of first n terms is, Sn =n2 2a + n - 1 d⇒ S7 =72 2a + 7 - 1 d [here, n = 7]⇒ 10 =72 2a + 6d⇒ 10 =7 a + 3d⇒ 7a + 21d = 10 ............1also, S14 = 1422a + (14 - 1)d = 7(2a + 13d) [Here n = 14]It is given that : S14 - S7 = 17⇒ 7 2a + 13d - 10 = 17⇒14a + 91d = 27 ..........(2)Multiply (1) by '2' , we get14a + 42d = 20 ........(3)Subtracting (3) from (2), we get49d = 7⇒ d = 749⇒ d = 17Substituting d =17 in (1), we get7a + 21 × 17 = 10⇒ 7a + 3 = 10⇒ 7a = 10 - 3⇒ 7a = 7⇒ a = 1Therefore a = 1 and d = 17 a8 = a + 7d = 1 + 7 × 17 = 1 + 1 = 2 3 View Full Answer Raghav answered this Here,The A.P.=a, a+d, a+2d.....a/c the sum of first seven terms is 10i.e. a+ a+d +a+2d +a+3d +a+4d +a+5d +a+6d =107a+21d=10Therefore, a=10-21d / 7 -(1)a/c the sum of next seven terms is 17i.e. a +7d +a+8d +a+9d +a+10d +a+11d +a+12d +a+13d =177a+ 70d=17By putting the value of a from eq. no. 17 (10- 21d / 7) +70d=1710 -21d+ 70d=1710+49d=17Therefore, d= 1/7By putting the value of d in eq. no. 1we get, a =1Now, a8=a+7d=1+ 7*1/7=1+1=2Hence, the eighth term of the A. P. is 2 3
