Calculus Examples

2

$2$ ,

4

$4$ ,

6

$6$

Step 1

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

2

$2$ 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 = 2

$d = 2$

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} = 2

$a_{1} = 2$ and

d = 2

$d = 2$ .

a_{n} = 2 + 2 (n - 1)

$a_{n} = 2 + 2 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 2 + 2 n + 2 \cdot - 1

$a_{n} = 2 + 2 n + 2 \cdot - 1$

Step 4.2

Multiply

2

$2$ by

- 1

$- 1$ .

a_{n} = 2 + 2 n - 2

$a_{n} = 2 + 2 n - 2$

a_{n} = 2 + 2 n - 2

$a_{n} = 2 + 2 n - 2$

Step 5

Combine the opposite terms in

2 + 2 n - 2

$2 + 2 n - 2$ .

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Step 5.1

Subtract

2

$2$ from

2

$2$ .

a_{n} = 2 n + 0

$a_{n} = 2 n + 0$

Step 5.2

Add

2 n

$2 n$ and

0

$0$ .

a_{n} = 2 n

$a_{n} = 2 n$

a_{n} = 2 n

$a_{n} = 2 n$

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