Answer:
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Use the sum of the first n terms formula:
- S = a₁ * (1 - rⁿ) / (1 - r) where a₁ is the first term, r is the common ratio, and n is the number of terms.
We are given:
First, let's find n using the nth term formula:
- aₙ = a₁ * rⁿ⁻¹
- 96 = 6 * 2ⁿ⁻¹
- 16 = 2ⁿ⁻¹
- 2⁴ = 2ⁿ⁻¹
- n - 1 = 4
- n = 5
Now, we can find the sum using the formula:
- S = 6 * (1 - 2⁵) / (1 - 2)
- S = 6 * (1 - 32) / (-1)
- S = 6 * 31
- S = 186
The sum of the geometric series is 186.