Calculus Examples

3

$3$ ,

9

$9$ ,

15

$15$ ,

21

$21$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

6

$6$ to the previous term in the sequence gives the next term. In other words,

a_{n} = a_{1} + d (n - 1)

$a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence:

d = 6

$d = 6$

Step 2

This is the formula of an arithmetic sequence.

a_{n} = a_{1} + d (n - 1)

$a_{n} = a_{1} + d (n - 1)$

Step 3

Substitute in the values of

a_{1} = 3

$a_{1} = 3$ and

d = 6

$d = 6$ .

a_{n} = 3 + 6 (n - 1)

$a_{n} = 3 + 6 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 3 + 6 n + 6 \cdot - 1

$a_{n} = 3 + 6 n + 6 \cdot - 1$

Step 4.2

Multiply

6

$6$ by

- 1

$- 1$ .

a_{n} = 3 + 6 n - 6

$a_{n} = 3 + 6 n - 6$

a_{n} = 3 + 6 n - 6

$a_{n} = 3 + 6 n - 6$

Step 5

Subtract

6

$6$ from

3

$3$ .

a_{n} = 6 n - 3

$a_{n} = 6 n - 3$

Step 6

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{5} = 6 (5) - 3

$a_{5} = 6 (5) - 3$

Step 7

Multiply

6

$6$ by

5

$5$ .

a_{5} = 30 - 3

$a_{5} = 30 - 3$

Step 8

Subtract

3

$3$ from

30

$30$ .

a_{5} = 27

$a_{5} = 27$

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