Question

A1=-3;an=an-1+7 what is the explicit rule of this sequence? an=​

Answer 1

`a_n=7n-10`

Explanation:

Without memorizing formulas for arithmetic sequences, it is best to list a first few terms, then realize that a part of each term is proportional to 7n ( a linear function). What remains to determine is the additive term (bias) based on the first value a1:

a1=-3

a2=4

a3=11

a4=18

`a_n=7(n-1)-3=7n-10`

Answer 2

`a_n=7n-10`

Explanation:

If
`a_1=-3` and
`a_n=a_(n-1)+7,` then

`a_2=a_1+7=-3+7=4,\\ \\a_3=a_2+7=4+7=11,\\ \\a_4=a_3+7=11+7=18,...`

So you get the sequence

`-3,\ 4,\ 11,\ 18,\ ...`

This is the arithmetic sequence with
`a_1=-3` and the difference
`d=7.`

The explicit formula of this sequence is

`a_n=a_1+(n-1)d,\\ \\a_n=-3+(n-1)\cdot7,\\ \\a_n=-3+7n-7,\\ \\a_n=7n-10.`