Question

Given the arithmetic sequence, find the term named in the problem -31, -35, -39, -43 Find a22

Answer 1

Step 1. The sequence that we have is:

`-31,-35,-39,-43`

This is an arithmetic sequence and we need to find the 22nd term.

Step 2. The formula that defines an arithmetic sequence is:

`a_n=a_1+d(n-1)`

where an is the value of the sequence for the nth term, a1 is the first term, and d is the difference between the terms.

In this case:

`a_1=-31`

Step 3. Finding d, the difference between the terms:

Thus, the value of d is -4:

`d=-4`

Step 4. Using the formula from step 2, we define a general equation for the sequence:

`\boxed{a_n=-31-4\left(n-1\right)}`

Using this equation, we can find any value of the sequence.

Step 5. Since we need to find the 22nd term, we take this value as the n value:

`n=22`

And substitute it into our equation:

`a_(22)=-31-4\left(22-1\right)`

Solving the operations:

`\begin{gathered} a_(22)=-31-4(21) \\ a_(22)=-31-84 \\ \boxed{a_(22)=-115} \end{gathered}`

Answer:

`\boxed{a_(22)=-115}`