Question

What is the nth term in the sequence -1, -4, -7, -10

Answer 1

It's an arithmetic sequence:

`a_1=-1\\a_2=a_1-3\to a_2=-1-3=-4\\a_3=a_2-3\to a_3=-4-3=-7\\a_4=a_3-3\to a_4=-7-3=-10\\\\a_1=-1,\ d=-3`

The general term of an arithmetic sequence is equal:

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

Substitute:

`a_n=-1+(n-1)(-3)` use distributive property

`a_n=-1+(n)(-3)+(-1)(-3)\\\\a_n=-1-3n+3\\\\a_n=2-3n`

Answer:
`\boxed{a_n=2-3n}`