Question

What is the sum of the geometric sequence 4, 16, 64, … if there are 8 terms?

21,845

43,690

65,535

87,380

Answer 1

the numbers are multiplied by 4.....
start with 4 (1st term)
4 (4) = 16 (2nd term)
16 (4) = 64 (3rd term)
64 (4) = 256 (4th term)
256 (4) = 1024 (5th term)
1024 (4) = 4096 (6th term)
4096 (4) = 16384 (7th term)
16384 (4) = 65536 (8th term)
Now you want the total, so just add...
4 + 16 + 64 + 256 + 1024 + 4096 + 16384 + 65536 = 87380

There is probably an easier way to do this....I just don't know it.
I couldn't have done this if there were 50 terms...lol

Answer 2

You can use the formula
\[S _{n}=\frac{a(r ^{n}-1)}{r-1}\]

Answer 3

Thank you!

Answer 4

You're welcome :)