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1. Find the first 5 terms of the following sequences: a) {an} = (n- 1)² b) b = 1, b2 = 2, bn = bn-1+2 bn-2 %3D %3D 2. Determine a formula for the sequence below, given the first 6 terms listed: {3,-6,9,-12, 15,-18...}

1. Find the first 5 terms of the following sequences: a) {an} = (n- 1)² b) b = 1, b2 = 2, bn = bn-1+2 bn-2 %3D %3D 2. Determine a formula for the sequence below, given the first 6 terms listed: {3,-6,9,-12, 15,-18...}

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Sequences - Educational Exercise** This exercise involves finding the first 5 terms of given sequences and determining a formula for a given sequence. **1. Find the first 5 terms of the following sequences:** **a) \(\{a_n\} = (n-1)^2\)** To find the first 5 terms, substitute \(n = 1, 2, 3, 4, 5\): - \(a_1 = (1-1)^2 = 0^2 = 0\) - \(a_2 = (2-1)^2 = 1^2 = 1\) - \(a_3 = (3-1)^2 = 2^2 = 4\) - \(a_4 = (4-1)^2 = 3^2 = 9\) - \(a_5 = (5-1)^2 = 4^2 = 16\) Thus, the first 5 terms are: \(0, 1, 4, 9, 16\). **b) \(b_1 = 1, b_2 = 2, b_n = b_{n-1} + 2 \cdot b_{n-2}\)** To find the first 5 terms, use the given initial values and the recurrence relation: - \(b_1 = 1\) - \(b_2 = 2\) - \(b_3 = b_2 + 2 \cdot b_1 = 2 + 2 \cdot 1 = 4\) - \(b_4 = b_3 + 2 \cdot b_2 = 4 + 2 \cdot 2 = 8\) - \(b_5 = b_4 + 2 \cdot b_3 = 8 + 2 \cdot 4 = 16\) Thus, the first 5 terms are: \(1, 2, 4, 8, 16\). **2. Determine a formula for the sequence below, given the first 6 terms listed: \(\{3, -6, 9, -12, 15, -18, \ldots\}\)** To identify a pattern, observe the given terms: \(3, -6, 9, -12,
Transcribed Image Text:**Sequences - Educational Exercise** This exercise involves finding the first 5 terms of given sequences and determining a formula for a given sequence. **1. Find the first 5 terms of the following sequences:** **a) \(\{a_n\} = (n-1)^2\)** To find the first 5 terms, substitute \(n = 1, 2, 3, 4, 5\): - \(a_1 = (1-1)^2 = 0^2 = 0\) - \(a_2 = (2-1)^2 = 1^2 = 1\) - \(a_3 = (3-1)^2 = 2^2 = 4\) - \(a_4 = (4-1)^2 = 3^2 = 9\) - \(a_5 = (5-1)^2 = 4^2 = 16\) Thus, the first 5 terms are: \(0, 1, 4, 9, 16\). **b) \(b_1 = 1, b_2 = 2, b_n = b_{n-1} + 2 \cdot b_{n-2}\)** To find the first 5 terms, use the given initial values and the recurrence relation: - \(b_1 = 1\) - \(b_2 = 2\) - \(b_3 = b_2 + 2 \cdot b_1 = 2 + 2 \cdot 1 = 4\) - \(b_4 = b_3 + 2 \cdot b_2 = 4 + 2 \cdot 2 = 8\) - \(b_5 = b_4 + 2 \cdot b_3 = 8 + 2 \cdot 4 = 16\) Thus, the first 5 terms are: \(1, 2, 4, 8, 16\). **2. Determine a formula for the sequence below, given the first 6 terms listed: \(\{3, -6, 9, -12, 15, -18, \ldots\}\)** To identify a pattern, observe the given terms: \(3, -6, 9, -12,
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