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