Calculus Examples

3

$3$ ,

7

$7$ ,

11

$11$

Step 1

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

4

$4$ 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 = 4

$d = 4$

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 = 4

$d = 4$ .

a_{n} = 3 + 4 (n - 1)

$a_{n} = 3 + 4 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 3 + 4 n + 4 \cdot - 1

$a_{n} = 3 + 4 n + 4 \cdot - 1$

Step 4.2

Multiply

4

$4$ by

- 1

$- 1$ .

a_{n} = 3 + 4 n - 4

$a_{n} = 3 + 4 n - 4$

a_{n} = 3 + 4 n - 4

$a_{n} = 3 + 4 n - 4$

Step 5

Subtract

4

$4$ from

3

$3$ .

a_{n} = 4 n - 1

$a_{n} = 4 n - 1$

Step 6

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{5} = 4 (5) - 1

$a_{5} = 4 (5) - 1$

Step 7

Multiply

4

$4$ by

5

$5$ .

a_{5} = 20 - 1

$a_{5} = 20 - 1$

Step 8

Subtract

1

$1$ from

20

$20$ .

a_{5} = 19

$a_{5} = 19$

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