9. Sequences, Series, & Induction

Geometric Sequences

9. Sequences, Series, & Induction

# Geometric Sequences - Video Tutorials & Practice Problems

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## Geometric Sequences - Recursive Formula

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Problem

ProblemWrite a recursive formula for the geometric sequence $\left\lbrace18,6,2,\frac23,\ldots\right\rbrace$.

A

$a_{n}=3a_{n-1}$

B

$a_{n}=\frac{a_{n-1}}{3}$

C

$a_{n}=18a_{n-1}$

D

$a_{n}=\frac23a_{n-1}$

3

concept

## Geometric Sequences - General Formula

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Problem

ProblemFind the $10^{\th}$ term of the geometric sequence in which $a_1=5$ and $r=2$.

A

5120

B

1280

C

10240

D

2560

5

Problem

ProblemWrite a formula for the general or $n^{\th}$ term of the geometric sequence where $a_7=1458$ and $r=-3$.

A

$a_{n}=1\cdot\left(-3\right)^{n-1}$

B

$a_{n}=2\cdot\left(-3\right)^{n-1}$

C

$a_{n}=-\frac23\cdot\left(-3\right)^{n-1}$

D

$a_{n}=\frac23\cdot\left(-3\right)^{n-1}$

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PRACTICE PROBLEMS AND ACTIVITIES (53)

- In Exercises 1–8, write the first five terms of each geometric sequence. a1 = 5, r = 3
- In Exercises 1–8, write the first five terms of each geometric sequence. a1 = 20, r = 1/2
- In Exercises 1–8, write the first five terms of each geometric sequence. an = - 4a_(n-1), a1 = 10
- In Exercises 1–8, write the first five terms of each geometric sequence. an = - 4a_(n-1), a1 = 10
- In Exercises 1–8, write the first five terms of each geometric sequence. an = - 5a_(n-1), a1 = - 6
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the ind...
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the ind...
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the ind...
- In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use t...
- In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use t...
- In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use t...
- Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the s...
- Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the s...
- Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the s...
- In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 3, r = 2
- In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric se...
- In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 1/2, r = 1/2
- In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric se...
- Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the ...
- In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric se...
- Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the ...
- In Exercises 37–44, find the sum of each infinite geometric series. 1 + 1/3 + 1/9 + 1/27 + ...
- Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the ...
- Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a(sub...
- In Exercises 37–44, find the sum of each infinite geometric series. 3 + 3/4 + 3/4^2 + 3/4^3 + ...
- Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135
- In Exercises 37–44, find the sum of each infinite geometric series. 1 - 1/2 + 1/4 - 1/8 + ...
- In Exercises 37–44, find the sum of each infinite geometric series. 1 - 1/2 + 1/4 - 1/8 + ...
- Use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum. *sigma not...
- In Exercises 37–44, find the sum of each infinite geometric series. ∞ Σ (i = 1) 8(- 0.3)^(i -- 1)
- In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.5 ̅ (repeating 5) = 5/10 ...
- Find the sum of each infinite geometric series. 2 - 1 + 1/2 - 1/4 + ...
- In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.47 ̅ (repeating 47) = 47/...
- Find the sum of each infinite geometric series. -6 + 4 - 8/3 + 16/9 - ...
- In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.257 ̅ (repeating 257)
- Express each repeating decimal as a fraction in lowest terms. 0.6 (repeating 6)
- Express each repeating decimal as a fraction in lowest terms. 0.6 (repeating 6)
- In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geo...
- In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geo...
- In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geo...
- In Exercises 57–62, let {a_n} = - 5, 10, - 20, 40, ..., {b_n} = 10, - 5, - 20, - 35, ..., {c_n} = - 2, 1, - 1...
- In Exercises 57–62, let {a_n} = - 5, 10, - 20, 40, ..., {b_n} = 10, - 5, - 20, - 35, ..., {c_n} = - 2, 1, - 1...
- In Exercises 63–64, find a2 and a3 for each geometric sequence. 8, a2, a3, 27
- In Exercises 63–64, find a2 and a3 for each geometric sequence. 2, a2, a3, - 54
- Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −...
- Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence whos...
- Exercises 88–90 will help you prepare for the material covered in the next section. Use the formula an = a₁3^(...