Domanda del libro di testo
Write the first three terms in each binomial expansion, expressing the result in simplified form. (x - 2y)10
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 9, Problema 31
Write the first five terms of each geometric sequence. a1 = 3, r = 2
Guida verificata passo dopo passo1
Identify the first term \(a_1\) and the common ratio \(r\) of the geometric sequence. Here, \(a_1 = 3\) and \(r = 2\).
Recall the formula for the \(n\)-th term of a geometric sequence: \(a_n = a_1 \times r^{n-1}\).
Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = 3 \times 2^{2-1} = 3 \times 2\).
Calculate the third term \(a_3\) by substituting \(n=3\): \(a_3 = 3 \times 2^{3-1} = 3 \times 2^2\).
Continue this process to find the fourth and fifth terms: \(a_4 = 3 \times 2^{4-1}\) and \(a_5 = 3 \times 2^{5-1}\).
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Geometric Sequence Definition
A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. This ratio remains the same throughout the sequence, creating a consistent pattern of growth or decay.
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Geometric Sequences - Recursive Formula
Common Ratio (r)
The common ratio is the fixed factor by which each term in a geometric sequence is multiplied to get the next term. In this problem, the ratio is 2, meaning each term is twice the previous term, which determines how the sequence progresses.
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Finding Terms of a Geometric Sequence
To find the nth term of a geometric sequence, use the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. Applying this formula allows you to calculate any term, including the first five terms as requested.
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4:18Geometric Sequences - Recursive Formula
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