Question

Simplify using distribution

Answer 1

Answer:
`a_n=7n-4` and
`a_n=2n-8`

Explanation:

1.
`a_n=3+7(n-1)` is an arithmetic sequence. The general rule is
`a_n=a_1+(n-1)d`

In the given expression, a1=3 and d=7. Distribute the 7 to terms in parentheses:

`a_n=3+7n-7\\a_n=7n-4\\`

Since it appears the nth term is not specified in the question, nothing will substituted for n.

2.
`a_n=-6+2(n-1)` is an arithmetic sequence. The general rule is
`a_n=a_1+(n-1)d`

In this expression, a1= -6 and d=2. Distribute the 2 to terms in parentheses:

`a_n=-6+2n-2\\a_n=2n-8\\`