Question

What is the explicit rule for this geometric sequence?

a1=4; an=13·an−1




an=4(1/3)n−1

an=1/3⋅4n

an=1/3⋅4^n−1

an=4(1/3)n

Answer 1

Anne found the 10th term of the following sequence. Her steps are shown below.

3, 7, 11, 15, …

1. common difference = 4, a1 = 3

2. an = 3 + (n - 1)4

3. an = 3 + 4n - 4

4. an = 4n - 1

5. a10 = 4(10) – 1

6. a10 = 39

Analyze Anne’s work. Is she correct? If not, what was her mistake?

Yes, she is correct.

No, she needed to find the common ratio because it is a geometric sequence.

No, she substituted the wrong values into the rule to find the equation that represented the sequence.

No, she solved for the 10th term incorrectly.

Explanation:

Answer 2

`\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^(n-1)\\------------------------------\\\text{We have the recursive form}\ a_1=4,\ a_n=(1)/(3)\cdot a_(n-1).\\\\\text{Therefore}\ r=(1)/(3).\ \text{Substitute:}\\\\\boxed{a_n=4\left((1)/(3)\right)^(n-1)}`