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.

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= 63722a+7-1d =632a+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 + 161S14 = 2241422a+14-1d =2242a+13d = 32        ........2Subtracting 1 from 2, we get    7d=14d=2  Putting d = 2 in 1, we get     2a + 12 = 182a = 6a = 3Now an=a+n-1dSo  a28=3+28-1×2 =3+54 = 57Hence, 28th term = 57

 

  • 66

S7 = 63

Snext 7 terms = 161

Total number of terms = 7+7 = 14

S14- S7 = Snext 7 terms

S14- 63 = 161

S14= 161 + 63 = 224

S7 = 7/2 ( 2a + d(7-1) )

63 = 7/2(2a + 6d)

Hence on solving you get 2a + 6d = 18 --------equation 1

S14 = 14/2( 2a + d(14-1))

224 = 7(2a + 13d)

2a + 13d = 32 ---------- equation 2

From equation 1 and 2

a = 3 and d = 2

Hence 28th term = a + d(n-1)

= 3 + 2(28-1)

= 3 + 54

= 57

  • 40
What are you looking for?