The sum of the 16th term of an AP is 240 and the sum of next 4 terms is 220. Find the 10th term

Answer 1

In AP sum of n terms is:

Sn = n [ 2 a + ( n - 1 ) d ] / 2

where

a = first term

d = common difference

In this case:

n = 16

S16 = 240

S16 = 16 [ 2 a + ( 16 - 1 ) d ] / 2

16 • ( 2 a + 15 d ) / 2 = 240

( 32 a + 240 d ) / 2 = 240

Multiply bith sides by 2

32 a + 240 d = 480

In AP an = a ( n - 1 ) d

a17 = a + 16 d

a18 = a + 17 d

a19 = a + 18 d

a20 = a + 19 d

The sum of next 4 terms is 220 means:

a17 + a18 + a19 + a20 = 220

a + 16 d + a + 17 d + a + 18 d + a + 19 d = 220

4 a + 70 d = 220

Now you must solve system of two equations:

32 a + 240 d = 480

4 a + 70 d = 220

The solution is:

a = - 15 , d = 4

10th term is:

a10 = a + 9 d = - 15 + 9 • 4 =

- 15 + 36 = 21