Question

How many terms of the ap 7,12,17 are needed to get the sum as 2542Also find the 31st term of the ap

Answer 1

Given series is 7,12,17..........

a=7, d=5, sum =2542, 

sum = (a+an/2)n

2542 = [7+(a+(n-1)d/2]n

2542 = [7+(7+(n-1)5)/2]n

2542*2 =(5n+9)n

5n^2+9n=5084

n=31//

a31=a+(n-1)d

a31=7+(31-1)5

=7+30*5

=7+150

ie, a31=157.