Algebra Examples

20

$20$ ,

15

$15$ ,

10

$10$ ,

5

$5$

Step 1

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

- 5

$- 5$ 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 = - 5

$d = - 5$

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} = 20

$a_{1} = 20$ and

d = - 5

$d = - 5$ .

a_{n} = 20 - 5 (n - 1)

$a_{n} = 20 - 5 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 20 - 5 n - 5 \cdot - 1

$a_{n} = 20 - 5 n - 5 \cdot - 1$

Step 4.2

Multiply

- 5

$- 5$ by

- 1

$- 1$ .

a_{n} = 20 - 5 n + 5

$a_{n} = 20 - 5 n + 5$

a_{n} = 20 - 5 n + 5

$a_{n} = 20 - 5 n + 5$

Step 5

Add

20

$20$ and

5

$5$ .

a_{n} = - 5 n + 25

$a_{n} = - 5 n + 25$