Sequences and Series · Ages 16–17
Sum of a Finite Geometric Sequence Worksheet
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Designed for 11th grade math students. Find the common ratio r, the first term a_1, and calculate the sum S_n using the formula S_n = a_1 * (1 - r^n) / (1 - r).
Find the common ratio r for the sequence: 2, 6, 18, 54.
Find the sum of the first 4 terms of the sequence: 5, 10, 20, 40.
Calculate the sum of the first 6 terms of the sequence: 4, 12, 36, ...
Find the sum of the first 5 terms of: 100, -50, 25, -12.5, ...
A sequence has a_1 = 7 and r = 2. Find the smallest n such that S_n > 100.
A student saves $10 the first week, and doubles the amount saved each week for 6 weeks. What is the total saved?
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Find the common ratio r for the sequence: 2, 6, 18, 54.
r = 3 (since 6 / 2 = 3).
Find the sum of the first 4 terms of the sequence: 5, 10, 20, 40.
S_4 = 5 * (1 - 2^4) / (1 - 2) = 5 * (1 - 16) / (-1) = 75.
Calculate the sum of the first 6 terms of the sequence: 4, 12, 36, ...
a_1 = 4, r = 3, n = 6. S_6 = 4 * (3^6 - 1) / (3 - 1) = 4 * (729 - 1) / 2 = 1,456.
Find the sum of the first 5 terms of: 100, -50, 25, -12.5, ...
a_1 = 100, r = -0.5, n = 5. S_5 = 100 * (1 - (-0.5)^5) / (1 - (-0.5)) = 100 * (1 - (-0.03125)) / 1.5 = 68.75.
A sequence has a_1 = 7 and r = 2. Find the smallest n such that S_n > 100.
n = 5. (S_4 = 7 * 15 = 105, which is already > 100; check S_3 = 49, S_4 = 105, so n = 4).
A student saves $10 the first week, and doubles the amount saved each week for 6 weeks. What is the total saved?
a_1 = 10, r = 2, n = 6. S_6 = 10 * (2^6 - 1) / (2 - 1) = 10 * (64 - 1) = $630.