Find the 5th Term 40 , 10 , -20 , -50

$40$ , $10$ , $- 20$ , $- 50$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 30$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 30$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 40$ and $d = - 30$ .

$a_{n} = 40 - 30 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 40 - 30 n - 30 \cdot - 1$

Multiply $- 30$ by $- 1$ .

$a_{n} = 40 - 30 n + 30$

Step 5

Add $40$ and $30$ .

$a_{n} = - 30 n + 70$

Step 6

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

$a_{5} = - 30 \cdot 5 + 70$

Step 7

Multiply $- 30$ by $5$ .

$a_{5} = - 150 + 70$

Step 8

Add $- 150$ and $70$ .

$a_{5} = - 80$

Find the 5th Term 40 , 10 , -20 , -50

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