The first term of an arithmetic sequence is 14. The 25 th term is 206. What is the common difference of the arithmetic sequence?

The common difference is 8

Explanation:

The first term of an arithmetic progression is 14 and the 25th term is 206. The formula to calculate for arithmetic progression is as follows:

Ap = a + (n-1) d

where

a = first term

n = number of term

d = common difference

a = 14

n = 25

Ap = 206

d = ?

The 25th term is 206, therefore,

206 = 14 + (25 - 1) d

206 = 14 + (24) d

collect like terms

206 - 14 = 24d

192 = 24d

divide both sides by 24

d = 192/24

d = 8

The common difference is 8

Given:

a1 (first term in arithmetic sequence) : 14

a25 (25th term in arithmetic sequence) : 206

Let d be the arithmetic difference

a25 = a1 + 24d

206 = 14 + 24 x d

Solving for d we get

d=8.

Thus the arithmetic difference is 8.