Question

BRAINLIEST, 5 STARS AND THANKS IF ANSWERED BOTH CORRECTLY. 1. What is the 8th term of the following geometric sequence? -8, 24, -72, 216.. A. 52, 488 B. 5,832 C. 17,496 D. -17,496 ---------- 2. What is the 6th term of the following geometric sequence? 2, -14, 98, -686... A. 33,614 B. -33,614 C. 235,298 D. -235,298

Answer 1

Answer:

C; B

Step-by-step explanation:

The direct/explicit formula for a geometric sequence is the following:

$a_n=a(r)^{n-1}$

Where aₙ represents the term n, a represents the initial value, and r represents the common ratio.

Therefore, to find the nth term, we just need to find the initial value and the common ratio.

1)

-8, 24, -72, 216...

The common ratio is the ratio between each consecutive term. Do two to confirm that they are indeed the same. Thus:

$r=24/-8=-3\\r=-72/24\stackrel{\checkmark}{=}-3$

So, the common ratio is -3. And the initial value is -8. Thus, putting them into our equation:

$a_n=-8(-3)^{n-1}$

Thus, the eighth term will be:

$a_8=-8(-3)^{8-1}\\a_8=-8(-3)^7\\a_8=17496$

C

2)

Again, find the common ratio.

2, -14, 98, -686...

$-14/2=-7\\98/-14\stackrel{\checkmark}{=}-7$

The common ratio is -7. The initial value is 2. Thus:

$a_n=2(-7)^{n-1}$

And the sixth term will be:

$a_6=2(-7)^{6-1}\\a_6=2(-7)^5\\a_6=-33614$

B