Sequences and Series · Ages 16–17
Sequences: General Terms and Recursive Rules Practice
Name: Date:
Use your knowledge of general and recursive definitions to solve each problem. Show all algebraic work.
Find the first four terms of the sequence given by the general term a_n = 2n + 5.
A sequence is defined recursively by a_1 = 3 and a_n = 2 * a_(n-1) - 1. Find the first four terms.
Write a general term formula for the sequence: 4, 7, 10, 13, 16...
Write a general term formula for the sequence: 2, 4, 8, 16, 32...
Given the formula a_n = 4n - 3, determine whether 93 is a term in the sequence. If so, find its position n.
Given the formula a_n = 5n + 2, determine whether 48 is a term in the sequence.
Determine whether the sequence a_n = 100 - 4n is increasing, decreasing, or not monotonic.
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Find the first four terms of the sequence given by the general term a_n = 2n + 5.
7, 9, 11, 13
A sequence is defined recursively by a_1 = 3 and a_n = 2 * a_(n-1) - 1. Find the first four terms.
3, 5, 9, 17
Write a general term formula for the sequence: 4, 7, 10, 13, 16...
a_n = 3n + 1
Write a general term formula for the sequence: 2, 4, 8, 16, 32...
a_n = 2^n
Given the formula a_n = 4n - 3, determine whether 93 is a term in the sequence. If so, find its position n.
Set 4n - 3 = 93. 4n = 96, so n = 24. Yes, 93 is the 24th term.
Given the formula a_n = 5n + 2, determine whether 48 is a term in the sequence.
Set 5n + 2 = 48. 5n = 46, so n = 46/5 = 9.2. Because n is not a whole number, 48 is not a term.
Determine whether the sequence a_n = 100 - 4n is increasing, decreasing, or not monotonic.
Decreasing, because a_(n+1) - a_n = [100 - 4(n+1)] - [100 - 4n] = -4, which is less than 0 for all n.