Objective
A geo
Definition
A geom
Example 1: Find the 8th Term
Problem: A geometric sequence has \(u_1 = 3\) and \(r = 2\). Find \(u_8\).
Answer: \(u_n = u_1 \cdot r^{n-1}\) \(u_8 = 3 \cdot 2^{8-1}\) \(\quad\ \ = 3 \cdot 2^7\) \(\quad\ \ = 3 \cdot 128\) \(\quad\ \ = 384\)
Example 2: Sum of First 5 Terms
Problem: Find the sum of the first 5 terms of the geometric series \(5 + 10 + 20 + \ldots\)
Answer: \(S_n = \frac{u_1(1 – r^n)}{1 – r}\) \(S_5 = \frac{5(1 – 2^5)}{1 – 2}\) \(\quad\ \ = \frac{5(1 – 32)}{-1}\) \(\quad\ \ = \frac{5(-31)}{-1}\) \(\quad\ \ = 155\)
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