Question

Given the arithmetic sequence bn with b1=6 and d=3, find b3.

Answer 1

Given:

In an arithmetic sequence
`b_n`,

`b_1=6,d=3`

To find:

The value of
`b_3`.

Solution:

In an arithmetic sequence
`b_n`,

First term :
`b_1=6`

Common difference :
`d=3`

The nth term of an AP is

`a_n=a+(n-1)d`

For given arithmetic sequence,

`b_n=b_1+(n-1)d`

Putting
`b_1=6,d=3`, we get

`b_n=6+(n-1)3`

`b_n=6+3n-3`

`b_n=3+3n`

Put n=3 to find the values of
`b_3`.

`b_3=3+3(3)`

`b_3=3+9`

`b_3=12`

Therefore, the value of
`b_3` is 12.