Precalculus Examples

1

$1$ ,

4

$4$ ,

7

$7$ ,

10

$10$

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} = 1

$a_{1} = 1$ and

d = 3

$d = 3$ .

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

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

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Apply the distributive property.

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

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

Step 4.2

Multiply

3

$3$ by

- 1

$- 1$ .

a_{n} = 1 + 3 n - 3

$a_{n} = 1 + 3 n - 3$

a_{n} = 1 + 3 n - 3

$a_{n} = 1 + 3 n - 3$

Step 5

Subtract

3

$3$ from

1

$1$ .

a_{n} = 3 n - 2

$a_{n} = 3 n - 2$

$1, 4, 7, 10$

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