Chapter 12: Q 37. (page 825)

In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{2} = 7; a_{4} = 1575$

Short Answer

Expert verified

The common ratio is $r = 15$ andlocalid="1646977238552" $a_{n} = \frac{7}{15} \cdot 15^{n - 1}$

Step by step solution

Step 1. Write the given information.

Given that $a_{2} = 7; a_{4} = 1575$

Step 2. Find the common ratio and a1.

The formula is $a_{n} = a_{1} \cdot r^{n - 1}$

localid="1646977214913" $a_{2} = a_{1} \cdot r^{2 - 1} 7 = a_{1} \cdot r a_{1} = \frac{7}{r} a_{4} = \frac{7}{2} \cdot r^{4 - 1} 1575 = \frac{7}{r} \cdot r^{3} 1575 = 7 r^{2} r^{2} = 225 r = 15 a_{1} = \frac{7}{15} a_{n} = \frac{7}{15} \cdot 15^{n - 1}$

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In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{2} = 7; a_{4} = 1575$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio and a1.

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In Problems 31–38, find the nth term anof each geometric sequence. When given, r is the common ratio.a2=7;a4=1575

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio and a1.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{2} = 7; a_{4} = 1575$