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 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

Answer 2

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