Algebra Examples

2

$2$ ,

8

$8$ ,

14

$14$ ,

20

$20$

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} = 2

$a_{1} = 2$ and

d = 6

$d = 6$ .

a_{n} = 2 + 6 (n - 1)

$a_{n} = 2 + 6 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 2 + 6 n + 6 \cdot - 1

$a_{n} = 2 + 6 n + 6 \cdot - 1$

Step 4.2

Multiply

6

$6$ by

- 1

$- 1$ .

a_{n} = 2 + 6 n - 6

$a_{n} = 2 + 6 n - 6$

a_{n} = 2 + 6 n - 6

$a_{n} = 2 + 6 n - 6$

Step 5

Subtract

6

$6$ from

2

$2$ .

a_{n} = 6 n - 4

$a_{n} = 6 n - 4$

Step 6

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{5} = 6 (5) - 4

$a_{5} = 6 (5) - 4$

Step 7

Multiply

6

$6$ by

5

$5$ .

a_{5} = 30 - 4

$a_{5} = 30 - 4$

Step 8

Subtract

4

$4$ from

30

$30$ .

a_{5} = 26

$a_{5} = 26$

2, 8, 14, 20

$2, 8, 14, 20$

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