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
Determine the sum of the first eight terms of the geometric series in which:
t1 = 42 and t9 = 10752
1 Answer
The sum of the first 8 terms is
Explanation:
The first step would be finding the common ratio.
If we take the geometric sequence with common ratio
#1, 2, 4, 8#
If given
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!