Calculus Examples

$5$ , $10$ , $15$ , $20$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 5$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 5$ and $d = 5$ .

$a_{n} = 5 + 5 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 5 + 5 n + 5 \cdot - 1$

Step 4.2

Multiply $5$ by $- 1$ .

$a_{n} = 5 + 5 n - 5$

Step 5

Combine the opposite terms in $5 + 5 n - 5$ .

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Step 5.1

Subtract $5$ from $5$ .

$a_{n} = 5 n + 0$

Step 5.2

Add $5 n$ and $0$ .

$a_{n} = 5 n$

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