Q: What represents the sum of a geometric series with 8 terms whose first term is 3 and common ratio is 4.
A: 65,535
Is my answer right? I wasn't sure when adding up the terms versus using Sigma notation.
How about just using the formula for Sn of a geometric sequence?
3(4^8-1)/(4-1) = 4^8-1 = 65535
To find the sum of a geometric series, you can use the formula:
S = a * (r^n - 1) / (r - 1)
where S represents the sum of the series, a represents the first term, r represents the common ratio, and n represents the number of terms.
In this case, the first term (a) is 3, the common ratio (r) is 4, and we have 8 terms, so n = 8.
Plugging these values into the formula:
S = 3 * (4^8 - 1) / (4 - 1)
= 3 * (65,536 - 1) / 3
= 3 * 65,535 / 3
= 65,535
So, your answer of 65,535 is correct.