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The first three terms of a geometric sequence are shown below.
What is the eighth term of the sequence?
A. -128x^8-384x^7
B. 128x^8+384x^7
C. 256x^9+768x^8
D. -256x^9-768x^8

The first three terms of a geometric sequence are shown below What is the eighth term of the sequence A 128x8384x7 B 128x8384x7 C 256x9768x8 D 256x9768x8 class=

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egenriether
Each term oscillates between positive and negative.  This always means there is a term (-1)⁽ⁿ⁺¹⁾ in there so that when n=1 we get (-1)²=1 and for n=2: (-1)3=-1.
This lets the terms switch signs.  Next, we see the first term is changing in magnitude by (2⁽ⁿ⁻¹⁾)xⁿ.  The last term is changing sign too and its magnitude is changing by 3(2x)⁽ⁿ⁻¹⁾.  Putting it together gives:
(-1)⁽ⁿ⁺¹⁾[(2⁽ⁿ⁻¹⁾)xⁿ + 3(2x)⁽ⁿ⁻¹⁾]  with n=8,
-1(2⁷x⁸ + 3(2⁷x⁷)) = -128x⁸ - 384x⁷
So A

Answer:

Option A is correct.

Step-by-step explanation:

Given:

First term, a = x + 3

second term = -2x² - 6x

Third term = 4x³ + 12x²

Common ratio, r = [tex]\frac{-2x^2-6x}{x+3}=\frac{-2x(x+3)}{x+3}=-2x[/tex]

nth term of GP is gievn by, [tex]a_n=ar^{n-1}[/tex]

So, Eight term = [tex]a_8=(x+3)(-2x)^{8-1}=(x+3)(-2x)^{7}=-128x^8-384x^7[/tex]

Therefore, Option A is correct.

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