Question

What is the 25th term of the arithmetic sequence where a1 = 8 and a9 = 48?

Answer 1

`a_25=128`

Explanation:

We know that ,

`color(blue)(n^(th)term " of the arithmetic sequence is :"`

`color(blue)(a_n=a_1+(n-1)d...to(I)`

We have ,

`color(red)(a_1=8 and a_9=48`

Using `(I)` ,we get

`=>a_9=a_1+(9-1)d=48`

`=>8+8d=48`

`=>8d=48-8=40`

`=>color(red)(d=5`

Again using `(I)` ,we get

`a_25=a_1+(25-1)d`

`=>a_25=8+24(5)`

`=>a_25=128`

Answer 2

`a_(25)=128`

Explanation:

`"the n th term of an arithmetic sequence is"`

`•color(white)(x)a_n=a_1+(n-1)d`

`"where d is the common difference"`

`"given "a_1=8" then"`

`a_9=8+8d=48rArr8d=40rArrd=5`

`a_(25)=8+(24xx5)=128`