Question

Two terms in a geometric sequence are a5=15 and a6=1.

What is the recursive rule that describes the sequence?

A.) a1=759,375; an=an−1⋅1/15

B.) a1=225; an=an−1⋅5

C.) a1=11,390,625; an=an−1⋅15

D.) none of these

E.) a1=50,625; an=an−1⋅1/5

Answer 1

Hello dear

your answer is option c

Answer 2

The recursive rule that describes the sequence is$a_{1} = 7,59,375; a_{n} = a_{n-1}.\frac{1}{15}$

Step-by-step explanation:

Given, two terms in a geometric sequence are $a_{5} = 15 \ and \ a_{6} = 1$

Common ratio = r = $\frac{1}{15}$

$a _{5} = 15\\=> a_{1}r^{5 - 1} = 15\\=>ar^{4} = 15\\=> a_{1}(\frac{1}{15})^{4} = 15\\=> a_{1}(\frac{1}{50625}) = 15\\=> a_{1} = 15\times 50625 = 7,59,375$

$a_{2} = a_{1}(\frac{1}{15})^{2-1}\\=> a_{n} = a_{n-1}.\frac{1}{15}$

Hence, the recursive rule that describes the sequence is$a_{1} = 7,59,375; a_{n} = a_{n-1}.\frac{1}{15}$