Domanda del libro di testo
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a60 when a1 = 35, d = -3.
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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 21
Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence. 1.5, - 3, 6, -12, ...
Guida verificata passo dopo passo1
Identify the first term of the geometric sequence, denoted as \(a_1\). In this sequence, the first term is \(1.5\).
Determine the common ratio \(r\) by dividing the second term by the first term: \(r = \frac{-3}{1.5}\).
Write the general formula for the \(n\)th term of a geometric sequence: \(a_n = a_1 \times r^{n-1}\).
Substitute the values of \(a_1\) and \(r\) into the formula to express \(a_n\) explicitly.
To find the seventh term \(a_7\), substitute \(n = 7\) into the formula: \(a_7 = a_1 \times r^{6}\).
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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, in the sequence 1.5, -3, 6, -12, ..., each term is multiplied by -2 to get the next term.
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Geometric Sequences - Recursive Formula
General Term Formula of a Geometric Sequence
The general term (nth term) of a geometric sequence is given by aₙ = a₁ * r^(n-1), where a₁ is the first term, r is the common ratio, and n is the term number. This formula allows you to find any term in the sequence without listing all previous terms.
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4:45Geometric Sequences - General Formula
Evaluating the nth Term
Once the general term formula is established, substitute the desired term number (n) into the formula to find that specific term. For example, to find the seventh term a₇, plug n = 7 into the formula and calculate the value.
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06:56Nth Roots
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