# Sequences - Video Tutorials & Practice Problems

## Introduction to Sequences

The first 4 terms of a sequence are $\left\lbrace\sqrt3,2\sqrt3,3\sqrt3,4\sqrt3,\ldots\right\rbrace$. Continuing this pattern, find the $7^{\th}$ term.

$8\sqrt3$

$6\sqrt3$

$7\sqrt3$

$9\sqrt3$

Determine the first 3 terms of the sequence given by the general formula

$a_{n}=\frac{1}{n!+1}$

$\left\lbrace\frac12,\frac13,\frac17\right\rbrace$

$\left\lbrace\frac12,\frac13,\frac14\right\rbrace$

$\left\lbrace1,2,7\right\rbrace$

$\left\lbrace1,\frac12,\frac16\right\rbrace$

## Writing a General Formula

## Example 1

## Example 2

## Recursive Formulas

Write the first 6 terms of the sequence given by the recursive formula $a_{n}=a_{n-2}+a_{n-1}$ ; $a_1=1$ ; $a_2=1$.

$\left\lbrace1,1,2,3,5,18\right\rbrace$

$\left\lbrace1,2,3,5,8,13\right\rbrace$

$\left\lbrace0,1,1,2,3,5\right\rbrace$

$\left\lbrace1,1,2,3,5,8\right\rbrace$

## Do you want more practice?

- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3n+2
- In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 7n - 4
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3^n
- In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−3)^n
- Evaluate 40!/(4! 38!)
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n(n+3)
- In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=2n/(n+4)
- In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3...
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1...
- The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequ...
- The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequ...
- The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequ...
- In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four ter...
- In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four ter...
- In Exercises 23–28, evaluate each factorial expression. 17!/15!
- In Exercises 23–28, evaluate each factorial expression. 16!/2!14!
- In Exercises 23–28, evaluate each factorial expression. (n+2)!/n!
- In Exercises 29–42, find each indicated sum. 6Σi=1 5i
- In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2
- In Exercises 29–42, find each indicated sum. 5Σk=1 k(k+4)
- In Exercises 29–42, find each indicated sum. 4Σi=1 (−1/2)^i
- In Exercises 29–42, find each indicated sum. 9Σi=5 11
- In Exercises 29–42, find each indicated sum. 4Σi=0 (−1)^i/i!
- In Exercises 29–42, find each indicated sum. 5Σi=1 i!/(i−1)!
- In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for...
- In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for...
- In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for...
- In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice a...
- In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice a...
- In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice a...
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5Σi=1 (a_i^2+1)
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5∑i=1 (2a_i+b_i)
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5Σi=1 (a_i+3b_i)
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5Σi=4 (a_i/b_i)^2
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5Σi=4 (a_i/b_i)^3
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5Σi=1 a_i^2+5Σi=1 b_i^2
- In Exercises 61–68, use the graphs of and to find each indicated sum. 5Σi=1 a_i^2−5Σi=3 b_i^2
- In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 200!/198!
- In Exercises 81–85, use a calculator's factorial key to evaluate each expression. (300/20)!
- In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/300
- In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/(20−3)!
- In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 54!/(54−3)!3!
- Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n...