Find the 6th Term 2 , 8 , 14 , 20

$2$ , $8$ , $14$ , $20$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $6$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 6$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 2$ and $d = 6$ .

$a_{n} = 2 + 6 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 2 + 6 n + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$a_{n} = 2 + 6 n - 6$

Step 5

Subtract $6$ from $2$ .

$a_{n} = 6 n - 4$

Step 6

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

$a_{6} = 6 (6) - 4$

Step 7

Multiply $6$ by $6$ .

$a_{6} = 36 - 4$

Step 8

Subtract $4$ from $36$ .

$a_{6} = 32$

Find the 6th Term 2 , 8 , 14 , 20

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