Algebra Examples

7

$7$ ,

14

$14$ ,

21

$21$ ,

28

$28$

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} = 7

$a_{1} = 7$ and

d = 7

$d = 7$ .

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

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

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

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

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

Step 4.2

Multiply

7

$7$ by

- 1

$- 1$ .

a_{n} = 7 + 7 n - 7

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

a_{n} = 7 + 7 n - 7

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

Step 5

Combine the opposite terms in

7 + 7 n - 7

$7 + 7 n - 7$ .

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Step 5.1

Subtract

7

$7$ from

7

$7$ .

a_{n} = 7 n + 0

$a_{n} = 7 n + 0$

Step 5.2

Add

7 n

$7 n$ and

0

$0$ .

a_{n} = 7 n

$a_{n} = 7 n$

a_{n} = 7 n

$a_{n} = 7 n$

7, 14, 21, 28

$7, 14, 21, 28$

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