Question

PLEASE!!!!! HELP ME!!!!!!

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

What is the recursive rule that describes the sequence?


A) a1=50,625; an=an−1⋅15

B) a1=11,390,625; an=an−1⋅15

C) a1=759,375; an=an−1⋅115

D) a1=225; an=an−1⋅5

Answer 1

Answer:

$15 = a_1 r^4$ (1)

$1 = a_1 r^5$ (2)

If we divide equations (2) and (1) we got:

$\frac{r^5}{r^4}= \frac{1}{15}$

And then $r= \frac{1}{15}$

And then we can find the value $a_1$ and we got from equation (1)

$a_1 = \frac{15}{r^4} = \frac{15}{(\frac{1}{15})^4} =759375$

And then the general term for the sequence would be given by:

$a_n = 759375 (\frac{1}{15})^n-1 , n=1,2,3,4,...$

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)

Step-by-step explanation:

the general formula for a geometric sequence is given by:

$a_n = a_1 r^{n-1}$

For this case we know that $a_5 = 15, a_6 = 1$

Then we have the following conditions:

$15 = a_1 r^4$ (1)

$1 = a_1 r^5$ (2)

If we divide equations (2) and (1) we got:

$\frac{r^5}{r^4}= \frac{1}{15}$

And then $r= \frac{1}{15}$

And then we can find the value $a_1$ and we got from equation (1)

$a_1 = \frac{15}{r^4} = \frac{15}{(\frac{1}{15})^4} =759375$

And then the general term for the sequence would be given by:

$a_n = 759375 (\frac{1}{15})^n-1 , n=1,2,3,4,...$

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)