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Find the fifth term of the geometric sequence with first term 2 and second term 1/4.

 Jul 17, 2020
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Use the formula for the nth term of a GS:

 

Nth term =First term x Common ratio^(Term number - 1)

 

1/4           = 2                 x     R^(2 - 1)

1/4           = 2                 x      R^1

Divide both sides by 2

(1/4) / 2  = R

1 / 8         = R, or:

R = 1 / 8 - Common ratio

 

5th term =First term x Common ratio^(term number - 1)

5th term = 2                x    (1 /8)^(5 - 1)

5th term = 2                x    (1/8)^4

5th term = 2                x      1 / 4096

5th term = 2 /4096 = 1 / 2048

 Jul 17, 2020

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