Question

The sum of 8th term of an A.P is 160 while to sum of the 20th term is 880. Find the 43rd term​

Answer 1

Let a and d be the first term and common difference, respectively. Then

the 8th term is a+7d
the 20th term is a+19d

The sum of the first 8 terms is
(a)+(a+d)+(a+2d)+...+(a+7d) = 8a+28d

The sum of the first 20 terms is
(a)+(a+d)+(a+2d)+...+(a+19d) = 20a+190d

So

8a + 28d = 160
20a+ 190d = 880

40a + 140d = 800
40a + 380d = 1760
240d = 960
d = 4

8a + 112 = 160
8a=48
a =
6

The first term is 6 and the common difference is 4.

The 43rd term is a+42d = 6+42(4) = 6+168 = 174

The sum of the first 12 terms is
(a)+(a+d)+(a+2d)+...+(a+11d) = 12a+66d = 12(6)+66(4) = 72+264 = 336