Question

what is the next term of the arithmetic sequence 24, 16, 8, 0, ...? and what is the explicit formula to find it?

Answer 1

Answer: We have an arithmetic sequence because the difference between the terms is constant:

$\begin{gathered} 0\rightarrow8\colon\Delta\rightarrow8 \\ 8\rightarrow16\colon\Delta\rightarrow8 \\ 16\rightarrow24\colon\Delta\rightarrow8 \end{gathered}$

From this the next term is simply:

$24+8=32$

And this sequence can be explicitly written as:

$a_n=a_1(n-1)d$

Where:

$\begin{gathered} a_n=nth\text{ term} \\ a_1=first\text{ term} \\ d=\text{distance betw}en\text{ the terms} \\ n=\text{any index number} \end{gathered}$

Therefore we have:

$\begin{gathered} a_n=1\cdot(n-1)8=8\cdot(n-1) \\ a_n=8\cdot(n-1) \end{gathered}$