Question

Find the sum of the first 25 terms of the following arithmetic sequence. Rather that write out each term use a Fourmula

a1=5,d=3

Answer 1

1025

Explanation

The formula to find the sum of the first n terms of an arithmetic sequence is

Sn = n/2 * [2a1 + (n-1)d]

Where

a1 = the first term of the sequence

d = the common difference between consecutive terms

n = the number of terms we want to sum

Substituting the given values, we get

a1 = 5

d = 3

n = 25

S25 = 25/2 * [2(5) + (25-1)3]

= 25/2 * [10 + 72]

= 25/2 * 82

= 25 * 41

= 1025