Algebra Examples

6

$6$ ,

9

$9$ ,

12

$12$ ,

15

$15$ ,

18

$18$

Step 1

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

3

$3$ 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 = 3

$d = 3$

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} = 6

$a_{1} = 6$ and

d = 3

$d = 3$ .

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

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

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

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

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

Step 4.2

Multiply

3

$3$ by

- 1

$- 1$ .

a_{n} = 6 + 3 n - 3

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

a_{n} = 6 + 3 n - 3

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

Step 5

Subtract

3

$3$ from

6

$6$ .

a_{n} = 3 n + 3

$a_{n} = 3 n + 3$

Step 6

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{6} = 3 (6) + 3

$a_{6} = 3 (6) + 3$

Step 7

Multiply

3

$3$ by

6

$6$ .

a_{6} = 18 + 3

$a_{6} = 18 + 3$

Step 8

Add

18

$18$ and

3

$3$ .

a_{6} = 21

$a_{6} = 21$