For each sequence, find a formula for the general term, an. Sequences start with n = 1. For example, answer n² if given the sequence: 1, 4, 9, 16, 25, 36,... an= 1 2n n+2 (n+3)² 1. 1 2468... 2./, 2 3 349 5
For each sequence, find a formula for the general term, an. Sequences start with n = 1. For example, answer n² if given the sequence: 1, 4, 9, 16, 25, 36,... an= 1 2n n+2 (n+3)² 1. 1 2468... 2./, 2 3 349 5
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 188E: In your own words, explain how to determine whether a sequence is geometric.
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![For each sequence, find a formula for the general term, \( a_n \). Sequences start with \( n = 1 \). For example, answer \( n^2 \) if given the sequence: 1, 4, 9, 16, 25, 36, \ldots
1. \[ a_n = \frac{1}{2^n} \]
Sequence: \( \frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \ldots \)
2. \[ a_n = \frac{n+2}{(n+3)^2} \]
Sequence: \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3c20d52-ca97-401f-9b18-f989c3a5b19f%2Fc96d9c5b-4769-4e5f-b764-af4c040996a3%2Fg8i720r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each sequence, find a formula for the general term, \( a_n \). Sequences start with \( n = 1 \). For example, answer \( n^2 \) if given the sequence: 1, 4, 9, 16, 25, 36, \ldots
1. \[ a_n = \frac{1}{2^n} \]
Sequence: \( \frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \ldots \)
2. \[ a_n = \frac{n+2}{(n+3)^2} \]
Sequence: \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots \)
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