In an arithmetic sequence the 15th term is -93 and the sum of first 15 terms is -660. What is the first term of the sequence?

Answer 1

a15=-53

s15 = -660

sn =n(a1+an)/2

a15 = 15(-53 +a1)/2 = 7.5(-53 +an) = -397.5 +15a1 = -397.5+15a1

15a1 = -660+397.5 = -262.5

a1 = -262.5/15

= - 52.5/3

= - 17.5 = 1st term of the AP

(a15-a1)/(15-1) = d = -53 +17.5)/14 = -35.5/14 = common difference