Question

The sum of first 20 terms of an arithmetic sequence is1060 and its 5th term is 20. Find the 15th term of sequence.

Answer 1

S²⁰ = 20/2 { 2a +19 d} = 10{ 2a +19 d}

=> 20a+190d =1060

=>2a+19d = 106 ........1

a⁵ = a+4d = 20 .........2

form eq2

a= 20-4d

put a for d

2a+19d = 106

2(20-4d) +19d = 106

40- 8d +19d =106

11d = 66

d= 6

put d for a

a = 20-4d = 20-4×6 = 20-24 = -4

hence the 15th term is a+14d = -4+14×6 = 80