Question

A recursive rule for an arithmetic sequence is a1=−3;an=an−1+7. What is an explicit rule for this sequence? Enter your answer in the box

Answer 1

an=a1+d(n-1)
a1=firs term
d=common difference
so

a1=-3
an=-3+d(n-1)

notice
an=a(n-1)+7
a2=a1+7
so therfor the common differece is 7


an=-3+7(n-1)
an=-3+7n-7
an=-10+7n

Answer 2

The explicit rule for the sequence is given by
`a_n=7n-10`

Explanation:

We have been given the recursive rule
`a_1=-3,a_n=a_(n-1)+7`

Let us find the second term by plugging n =2 in the recursive rule.

`a_2=a_1+7\\a_2=-3+7\\a_2=4`

Therefore, the common difference of the arithmetic sequence is given by

`d=a_2-a_1\\d=4-(-3)\\d=7`

Therefore, the explicit rule for the sequence is given by

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