Find the number of terms of the arithmetic sequence with the

Find the number of terms of the arithmetic sequence with the given description that must be added to get a value of 2700. The first term is 5, and the common difference is 2.

Solution

The sum of n terms of arithmetic series is given by

S_n= (n/2)(2a+ (n-1)d)

Here S_n=2700

a=5

d=2

2700=n/2(10+ (n-1)2)

5400=n(2n+8)

2n²+8n -5400=0

n²+4n -2700=0

(n-50)(n+54)=0

n=50,-54

Number of terms cant be negative

Hence the answer is n=50