The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P. Share with your friends Share 21 Utsav answered this Let the first term of A.P be a and common difference be d. As we know that sum of n terms of an A.P be Sn =n22a+n-1dNow, sum of first 7 terms = 63⇒ S7= 63⇒722a+7-1d =63⇒2a+6d =18 ......1We have,sum of next 7 terms = 161So, sum of first 14 terms = sum of first 7 terms + sum of next 7 terms S14 = 63 + 161⇒S14 = 224⇒1422a+14-1d =224⇒2a+13d = 32 ........2Subtracting 1 from 2, we get 7d=14⇒d=2 Putting d = 2 in 1, we get 2a + 12 = 18⇒2a = 6⇒a = 3Now an=a+n-1dSo a28=3+28-1×2 =3+54 = 57Hence, 28th term = 57 66 View Full Answer Shruti Sriram answered this S7 = 63Snext 7 terms = 161Total number of terms = 7+7 = 14S14- S7 = Snext 7 termsS14- 63 = 161S14= 161 + 63 = 224S7 = 7/2 ( 2a + d(7-1) )63 = 7/2(2a + 6d)Hence on solving you get 2a + 6d = 18 --------equation 1S14 = 14/2( 2a + d(14-1))224 = 7(2a + 13d)2a + 13d = 32 ---------- equation 2From equation 1 and 2 a = 3 and d = 2Hence 28th term = a + d(n-1) = 3 + 2(28-1) = 3 + 54 = 57 40