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lubasha [3.4K]
4 years ago
15

The first three terms of a geometric sequence are shown below.

Mathematics
2 answers:
san4es73 [151]4 years ago
4 0
This is a geometric sequence of the form:

a(n)=(x+3)(-2x)^(n-1)  because each term is -2x times the previous term...so

a(8)=(x+3)(-128x^7)

a(8)=-128x^8-384x^7
Elis [28]4 years ago
4 0

Answer:

a_8=-128x^8-384x^{7}

Step-by-step explanation:

G.P. = x+3,-2x^2-6x,4x^3+12x^2+...

So, first term = a=x+3

Common ratio = r =\frac{a_2}{a_1}

                       = \frac{-2x^2-6x}{x+3}

                       = \frac{-2x(x+3)}{x+3}

                       = -2x

So, r = -2x

nth term of G.P. = a_n=ar^{n-1}

Substitute n = 8

a_8=(x+3)(-2x)^{8-1}

a_8=(x+3)(-2x)^{7}

a_8=(x+3)(-128)(x)^{7}

a_8=-128x^8-384x^{7}

Hence the eighth term of the sequence is  a_8=-128x^8-384x^{7}

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