Answer:
The sum of the first seven terms of this geometric series is - 32,766
Explanation:
Let's find out the result of the sum of a 7-term geometric series, which first term is -6, the last term is -24576, and the common ratio is 4
1st term = - 6
2nd term = - 6 * 4 = - 24
3rd term = - 24 * 4 = - 96
4th term = - 96 * 4 = - 384
5th term = - 384 * 4 = - 1,536
6th term = - 1,536 * 4 = - 6,144
7th term = - 6,144 * 4 = - 24,576
Sum = - 24,576 - 6,144 - 1,536 - 384 - 96 - 24 - 6
Sum = - 32,766
We can summarize these operations of the geometric series, this way:
Sₙ= a₁ * (1 − rⁿ)/1 − r, where:
n = Number of terms of the series
a₁ = First term of the series
r = Common ratio
Replacing with the real values, we have:
S₇= -6 * (1 −4⁷)/1 - 4
S₇= -6 * (1 − 16,384)/ -3
S₇= -6 * ( − 16,383)/ -3
S₇= 98,298/ -3
S₇= - 32,766
The sum of the first seven terms of this geometric series is - 32,766