Solve the sum of 8 terms in a geometric series?

Determine the sum of the first eight terms of the geometric series in which:

t1 = 42 and t9 = 10752

1 Answer
Noah G
Jan 8, 2018

The sum of the first 8 terms is #10710#

Explanation:

The first step would be finding the common ratio.

If we take the geometric sequence with common ratio #2# and terms

#1, 2, 4, 8#

If given #t_1 = 1# and #t_4 = 8#, we can say that the common ratio is used #3# times, thus the common ratio is equivalent to #root(3)(8/1) = 2#, which is clear when we write out all #4# terms.

Applying this concept to our given problem, we see that

#r = root(8)(10752/42) = root(8)(256) = 2#

We know that the sum of a geometric series is given by

#S_n = (a(1 - r^n))/(1 - r)#

Applying this to our problem we get

#S_8 = (42(1 - 2^8))/(1 - 2)#

#S_8 = -42(1 - 2^8)#

#S_8 = 10710#

Hopefully this helps!

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