What is the sum of a 7-term geometric series if the first term is -6, the last term is -24576, and the common ratio is 4?

The sum of the first seven terms of this geometric series is - 32,766

Step-by-step 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

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70.30

step-by-step explanation: