Question

I need help writing the first 5 terms of the sequence!

Answer 1

The first five terms of the sequence are 1, 4, 7, 10, 13.

Solution:

Given data:

`a_(1)=1`

`a_(n)=a_(n-1)+3`

General term of the arithmetic sequence.

`a_(n)=a_(n-1)+d`, where d is the common difference.

d = 3

`a_(n)=a_(n-1)+3`

Put n = 2 in
`a_(n)=a_(n-1)+3`, we get

`a_(2)=a_1+3`

`a_(2)=1+3`

`a_2=4`

Put n = 3 in
`a_(n)=a_(n-1)+3`, we get

`a_(3)=a_2+3`

`a_(3)=4+3`

`a_3=7`

Put n = 4 in
`a_(n)=a_(n-1)+3`, we get

`a_(4)=a_3+3`

`a_(4)=7+3`

`a_4=10`

Put n = 5 in
`a_(n)=a_(n-1)+3`, we get

`a_(5)=a_4+3`

`a_(5)=10+3`

`a_5=13`

The first five terms of the sequence are 1, 4, 7, 10, 13.