Question

Create an arithmetic sequence up to 5 terms. Then find the explicit formula for the nth term.

Answer 1

The explicit formula for the nth term of an arithmetic sequence:

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

d - common difference

Create an arithmetic sequence:

`a_1=1\\\\a_2=1+2=3\\\\a_3=3+2=5\\\\a_4=5+2=7\\\\a_5=7+2=9\\\\1,\ 3,\ 5,\ 7,\ 9`

`a_1=1,\ d=2`

Substitute:

`a_n=1+(n-1)(2)=1+2n-2=2n-1`

Answer:
`\boxed{a_n=2n-1}`