The sum of the first two five terms of a geometric series is 3798 and the sum to infinity is 4374. Find the sum of the first seven terms.?
+130516 The sum of the first two five terms of a geometric series is 3798
Which is it???...two, five [or maybe twenty five ???]
+23254 If you assume that the word "two" is a typo, and have the problem that the sum of the first five terms is 3798 while the sum to infinity is 4374:
The formula for the sum of the first five terms of a geometric series is: Sum = a(r5 - 1) / (r - 1).
The formula for the sum of an infinite geometric series is: InfSum = a/(1 - r) with |r| < 1.
We have: a(r5 - 1) / (r - 1) = 3798 and a/(1 - r) = 4374
Since a/(1 - r) = 4374 ---> a/(r - 1) = -4374
Since a(r5 - 1) / (r - 1) = 3798 ---> [1/(r - 1)] x (r5 - 1) = 3798 ---> -4374 x (r5 - 1) = 3798
---> r5 - 1 = -3798/4374 ---> r5 = 1 - 3798/4374 ---> r5 = 576/4374 = 32/243 ---> r = 2/3
Knowing that r = 2/3: a/(1 - r) = 4374 ---> a/(1 - 2/3) = 4374 ---> a/(1/3) = 4374 ---> a = 1458
To find the sum of the first seven terms: Sum = a(r7 - 1) / (r - 1) = 1458( (2/3)7 - 1 ) / ( 2/3 - 1 ) = 4188
