Calculus Examples

$3$ , $7$ , $11$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $4$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 4$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 3$ and $d = 4$ .

$a_{n} = 3 + 4 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 3 + 4 n + 4 \cdot - 1$

Step 4.2

Multiply $4$ by $- 1$ .

$a_{n} = 3 + 4 n - 4$

Step 5

Subtract $4$ from $3$ .

$a_{n} = 4 n - 1$

Step 6

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

$a_{5} = 4 (5) - 1$

Step 7

Multiply $4$ by $5$ .

$a_{5} = 20 - 1$

Step 8

Subtract $1$ from $20$ .

$a_{5} = 19$

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