Question

How many terms of an A.P. 7 , 14 , 21 ....... are needed to give sum 5740.

Answer 1

Given series 7 , 14 , 21 , .......
first term ,a=7
common difference,d =7
use formula ,
Sn=n/2 {2a +(n-1) d}
5740 =n/2 {2*7 +(n-1)*7}
5740*2=11480 =14n + 7n² - 7n
=7n + 7n²
n² + n =11480/7=1640
n² + n -1640= 0
use quadratic formula ,
n=-b+_√(b²-4ac)/2a=-1+_√(1+6560)/2
=(-1+_81)/2 =40, -41

hence n=40