Question

What is the 8th term of the geometric sequence 4, -20, 100, ...?

Answer 1

Answer: Choice A) -312,500

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The long way to find the answer is to multiply each term by -5 until you've generated 8 terms total.

4 is the first term

-20 is the second term (4 times -5 = -20)

100 is the third term (-20 times -5 = 100)

100 times -5 = -500 which is the fourth term

-500 times -5 = 2500 which is the fifth term

2500 times -5 = -12500 which is the sixth term

-12500 times -5 = 62500 which is the seventh term

62500 times -5 = -312500 which is the eigth term

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A shortcut is to use the formula below

a(n) = a*(r)^(n-1)

Plug in a = 4, r = -5 and n = 8

a(n) = a*(r)^(n-1)

a(8) = 4*(-5)^(8-1)

a(8) = 4*(-5)^7

a(8) = 4*(-78125)

a(8) = -312,500

and we get the same answer