Find the 5th Term 16 , 48 , 80

$16$ , $48$ , $80$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $32$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 32$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 16$ and $d = 32$ .

$a_{n} = 16 + 32 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 16 + 32 n + 32 \cdot - 1$

Multiply $32$ by $- 1$ .

$a_{n} = 16 + 32 n - 32$

Step 5

Subtract $32$ from $16$ .

$a_{n} = 32 n - 16$

Step 6

Substitute in the value of $n$ to find the $n$ th term.

$a_{5} = 32 (5) - 16$

Step 7

Multiply $32$ by $5$ .

$a_{5} = 160 - 16$

Step 8

Subtract $16$ from $160$ .

$a_{5} = 144$

Find the 5th Term 16 , 48 , 80

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