Calculus Examples

$0$ ,

$4$ ,

$8$ ,

$12$ ,

$16$

Step 1

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

$4$ to the previous term in the sequence gives the next term. In other words,

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

Arithmetic Sequence:

$d = 4$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of

$a_{1} = 0$ and

$d = 4$ .

$a_{n} = 0 + 4 (n - 1)$

Step 4

Add

$0$ and

$4 (n - 1)$ .

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

Step 5

Apply the distributive property.

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

Step 6

Multiply

$4$ by

$- 1$ .

$a_{n} = 4 n - 4$

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