Question

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

Answer 1

The common difference is 8

Step-by-step 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

Answer 2

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.