Algebra Examples

1

$1$ ,

3

$3$ ,

5

$5$ ,

7

$7$ ,

9

$9$

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} = 1

$a_{1} = 1$ and

d = 2

$d = 2$ .

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

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

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

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

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

Step 4.2

Multiply

2

$2$ by

- 1

$- 1$ .

a_{n} = 1 + 2 n - 2

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

a_{n} = 1 + 2 n - 2

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

Step 5

Subtract

2

$2$ from

1

$1$ .

a_{n} = 2 n - 1

$a_{n} = 2 n - 1$

Step 6

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{6} = 2 (6) - 1

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

Step 7

Multiply

2

$2$ by

6

$6$ .

a_{6} = 12 - 1

$a_{6} = 12 - 1$

Step 8

Subtract

1

$1$ from

12

$12$ .

a_{6} = 11

$a_{6} = 11$

1, 3, 5, 7, 9

$1, 3, 5, 7, 9$

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