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Find the sum of the geometric sequence. 4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3

User Wondra
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1 Answer

3 votes

Answer:

Sum =
(1364)/(3)

Explanation:

The given geometric sequence is:


(4)/(3), (16)/(3), (64)/(3), (256)/(3),(1024)/(3)

The first term of the sequence is
a_(1)=(4)/(3)

The common ratio of the sequence is:


r=((16)/(3) )/((4)/(3) )=4

There are 5 terms in total in the given sequence so n = 5

The formula to calculate the sum of finite geometric sequence is:


S_(n) = (a_(1)(1-r^(n)) )/(1-r)

Using the given values, we get:


S_(5)=((4)/(3) (1-4^(5)) )/(1-5) = (1364)/(3)

Therefore, the sum of given geometric sequence is
(1364)/(3)

User Don Lockhart
by
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