Question

Find an equation for the nth term of the arithmetic sequence.
-1, 2, 5, 8, ...

Answer 1

-1 + 3(n-1)
hope this helps you

Answer 2

The expression for the n-th term is
`a_n = -4+3n.`

Explanation:

We know that the n-th term of an arithmetic progression is given by
`a_n= a+nd`. So we need to find the coefficients
`a` and
`d`. In order to do this, we substitute the values
`n=1` and
`n=2` in the expression for
`a_n`:

`a_1 = a+d    = -1,`

`a_2 = a+2d = 2.`

Now, notice that we have two linear equations with two unknowns, which it is not difficult to solve. Thus, the solution is
`d=3` and
`a=-4`.

Hence, the expression for the n-th term is
`a_n = -4+3n.`

We can check that the expression is correct substituting the values
`n=3` which gives
`a_3 = 5` and
`n=4` which gives
`a_4 = 8`, as it is given in the statement of the problem.