Algebra Examples

6

$6$ ,

13

$13$ ,

20

$20$ ,

27

$27$ ,

34

$34$

Step 1

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

7

$7$ 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 = 7

$d = 7$

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 = 7

$d = 7$ .

a_{n} = 6 + 7 (n - 1)

$a_{n} = 6 + 7 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 6 + 7 n + 7 \cdot - 1

$a_{n} = 6 + 7 n + 7 \cdot - 1$

Step 4.2

Multiply

7

$7$ by

- 1

$- 1$ .

a_{n} = 6 + 7 n - 7

$a_{n} = 6 + 7 n - 7$

a_{n} = 6 + 7 n - 7

$a_{n} = 6 + 7 n - 7$

Step 5

Subtract

7

$7$ from

6

$6$ .

a_{n} = 7 n - 1

$a_{n} = 7 n - 1$