Calculus Examples

$8$ , $16$ , $24$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $8$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 8$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 8$ and $d = 8$ .

$a_{n} = 8 + 8 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 8 + 8 n + 8 \cdot - 1$

Step 4.2

Multiply $8$ by $- 1$ .

$a_{n} = 8 + 8 n - 8$

Step 5

Combine the opposite terms in $8 + 8 n - 8$ .

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Step 5.1

Subtract $8$ from $8$ .

$a_{n} = 8 n + 0$

Step 5.2

Add $8 n$ and $0$ .

$a_{n} = 8 n$

Step 6

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

$a_{4} = 8 (4)$

Step 7

Multiply $8$ by $4$ .

$a_{4} = 32$

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