Question

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

Answer 1

an = a1+ d(n-1)

a1 =14

an=206  when n=25

206 = 14 + d (25-1)

206 = 14 + d * 24

subtract 14 from each side

192 = 24d

divide by 24 on each side

d=8

The common difference is 8

Answer 2

an atirmetic sequence  can be written in form

$a_n=a_1+d(n-1)$

where $a_n$ is the nth term

$a_1$ is the first term

$d$ is the common difference

$n$ is the counter variable

so, given that first term is 14 ($a_1=14$) and given taht 25th term is 206 ($a_{25}=206$), we want to find d

$a_{25}=206$

$a_{25}=a_1+d(25-1)$

$206=14+24d$

minus 14 both sides

$192=24d$

divide both sides by 24

$8=d$

the common difference is 8