Question

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

Answer 1

Answer:

$a_n=7n-10$

Step-by-step 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

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

Answer 2

Answer:

$a_n=7n-10$

Step-by-step 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

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