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

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 Link

SociometricStar SociometricStar · Answer 2 · 2018-12-11T09:34:23+01:00

Answer:

The explicit rule for the sequence is given by [tex]a_n=7n-10[/tex]

Step-by-step explanation:

We have been given the recursive rule [tex]a_1=-3,a_n=a_{n-1}+7[/tex]

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

[tex]a_2=a_1+7\\a_2=-3+7\\a_2=4[/tex]

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

[tex]d=a_2-a_1\\d=4-(-3)\\d=7[/tex]

Therefore, the explicit rule for the sequence is given by

[tex]a_n=a_1+(n-1)d\\a_n=-3+(n-1)7\\a_n=-3+7n-7\\a_n=7n-10[/tex]