Final answer:
To find the 16th term of a geometric sequence with given terms, use the formula aₙ = a₁ * r^(n-1), and solve for r. Substitute the values into the formula to find the desired term.
Step-by-step explanation:
To find the 16th term of a geometric sequence, we can use the formula:
aₙ = a₁ * r^(n-1)
Where a₁ is the first term, r is the common ratio, and n is the term number.
Given that a₁ = 4 and aₙ = -8,748, we can rearrange the formula to solve for r:
-8,748 = 4 * r^(16-1)
Dividing both sides by 4:
r^(15) = -8,748/4 = -2,187
Taking the 15th root of both sides:
r = (-2,187)^(1/15)
Now we can substitute the values into the formula to find the 16th term:
aₙ = 4 * ((-2,187)^(1/15))^(16-1)
Calculating this expression will give us the 16th term of the geometric sequence.
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