Precalculus Examples

$- 11.5$ , $- 7.7$ , $- 3.9$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $3.8$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 3.8$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = - 11.5$ and $d = 3.8$ .

$a_{n} = - 11.5 + 3.8 (n - 1)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Apply the distributive property.

$a_{n} = - 11.5 + 3.8 n + 3.8 \cdot - 1$

Step 4.2

Multiply $3.8$ by $- 1$ .

$a_{n} = - 11.5 + 3.8 n - 3.8$

Step 5

Subtract $3.8$ from $- 11.5$ .

$a_{n} = 3.8 n - 15.3$

Step 6

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

$a_{4} = 3.8 (4) - 15.3$

Step 7

Multiply $3.8$ by $4$ .

$a_{4} = 15.2 - 15.3$

Step 8

Subtract $15.3$ from $15.2$ .

$a_{4} = - 0.1$