Question

I need help solving this practice problem for my calculus prep guide

Answer 1

Okay, here we have this:

Considering the provided terms, we are going to identify the formula of the arithmetic sequence and later we will calculate the term number 84, so we obtain the following:

Difference=a2-a1=-1269-(-1286)

Difference=-1269+1286

Difference=17

Now, let's replace in the arithmetic sequence form, so we have the following sequence:

`\begin{gathered} a_n=a_1+\mleft(n-1\mright)d \\ a_n=-1286+(n-1)17 \\ a_n=-1286+17n-17 \\ a_n=17n-1303 \end{gathered}`

Finally, let's replace with n=84, then:

`\begin{gathered} a_(84)=17\mleft(84\mright)-1303 \\ =1428-1303 \\ =125 \end{gathered}`

Finally we obtain that the 84th term of the sequence is 125.