Question

Find a formula for the nth term in this

arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
an

Answer 1

an = 7 -3(n -1)

Explanation:

You want the formula for the n-th term of the arithmetic sequence 7, 4, 1, -2, ....

Arithmetic sequence

An arithmetic sequence has a first term (a1) and a common difference (d) found by subtracting the previous term from the current term.

In the given sequence, the first term is a1=7, and the common difference is d=(a2 -a1) = 4 -7 = -3.

The n-th term of the given arithmetic sequence is ...

`a_n=a_1+d(n-1)\\\\\boxed{a_n=7-3(n-1)}`

__

Additional comment

The formula can be simplified to ...

an = 10 -3n