In a geometric sequence, the third term is 18 and the sixth term is 486. What is the sum of the first 8 terms?
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Correct answer
B. 6560
Principle or equation
For a geometric sequence with first term a and common ratio r, the nth term is a * r^(n-1). The sum of the first n terms is a * (r^n - 1) / (r - 1) for r ≠ 1.
Why this answer is correct
Let the first term be a and common ratio r. Then a * r^2 = 18 and a * r^5 = 486. Dividing the second by the first gives r^3 = 27, so r = 3. Then a * 9 = 18, so a = 2. The sum of the first 8 terms is 2 * (3^8 - 1) / (3 - 1) = 2 * (6561 - 1) / 2 = 6560.
Example
If a geometric sequence has first term 3 and common ratio 2, the sum of the first 4 terms is 3 * (2^4 - 1)/(2-1) = 3 * 15 = 45.
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