Algebra Examples

42

$42$ ,

38

$38$ ,

34

$34$ ,

30

$30$

Step 1

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

- 4

$- 4$ 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 = - 4

$d = - 4$

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} = 42

$a_{1} = 42$ and

d = - 4

$d = - 4$ .

a_{n} = 42 - 4 (n - 1)

$a_{n} = 42 - 4 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

a_{n} = 42 - 4 n - 4 \cdot - 1

$a_{n} = 42 - 4 n - 4 \cdot - 1$

Step 4.2

Multiply

- 4

$- 4$ by

- 1

$- 1$ .

a_{n} = 42 - 4 n + 4

$a_{n} = 42 - 4 n + 4$

a_{n} = 42 - 4 n + 4

$a_{n} = 42 - 4 n + 4$

Step 5

Add

42

$42$ and

4

$4$ .

a_{n} = - 4 n + 46

$a_{n} = - 4 n + 46$

Step 6

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{5} = - 4 \cdot 5 + 46

$a_{5} = - 4 \cdot 5 + 46$

Step 7

Multiply

- 4

$- 4$ by

5

$5$ .

a_{5} = - 20 + 46

$a_{5} = - 20 + 46$

Step 8

Add

- 20

$- 20$ and

46

$46$ .

a_{5} = 26

$a_{5} = 26$

42, 38, 34, 30

$42, 38, 34, 30$

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