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notsponge [240]
4 years ago
9

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
Mathematics
1 answer:
sattari [20]4 years ago
6 0

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 <em>aₙ </em>represents the term <em>n</em>, <em>a</em> represents the initial value, and <em>r</em> represents the common ratio.

Therefore, to find the <em>nth</em> 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

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