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Use the formula for nCr to evaluate each expression. 11C4
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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 11
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a12 when a1 = 5, r = - 2
Guida verificata passo dopo passo1
Recall the formula for the nth term of a geometric sequence: \(a_n = a_1 \times r^{n-1}\), where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.
Identify the given values: the first term \(a_1 = 5\), the common ratio \(r = -2\), and the term to find is the 12th term, so \(n = 12\).
Substitute the known values into the formula: \(a_{12} = 5 \times (-2)^{12-1}\).
Simplify the exponent expression: calculate the power \((-2)^{11}\), keeping in mind the sign and magnitude.
Multiply the first term by the result of the exponentiation to express \(a_{12}\) fully as \(5 \times (-2)^{11}\).
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Geometric Sequence
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. For example, if the first term is 5 and the ratio is -2, the sequence progresses as 5, -10, 20, and so on.
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Geometric Sequences - Recursive Formula
General Term Formula of a Geometric Sequence
The nth term of a geometric sequence can be found using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number. This formula allows direct calculation of any term without listing all previous terms.
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4:45Geometric Sequences - General Formula
Exponentiation and Negative Ratios
When the common ratio is negative, powers of the ratio alternate in sign depending on whether the exponent is even or odd. Understanding how to handle negative bases raised to integer powers is essential to correctly compute terms like a_12 in the sequence.
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6:13Exponential Functions
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