Question

In the following exercise, find a general term for the sequence whose first five terms are shown.

8, 16, 24, 32, 40, …

Short answer

The general term for the sequence whose first five terms are 8, 16, 24, 32, 40, … is$a_n=8n.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thefirstfivetermsofthesequenceare}\\ 8,16,24,32,40,\dots \\ \text{Wehavetofindthegeneraltermforthesequence.}\end{array}$

Step 2. Observing the pattern

Now,

$\begin{array}{llllllll}n:& 1& 2& 3& 4& 5& \mathrm{...}& n\\ \text{Terms}& 8& 16& 24& 32& 40& \mathrm{...}& \\ \text{Pattern}& 8\cdot 1& 8\cdot 2& 8\cdot 3& 8\cdot 4& 8\cdot 5& \mathrm{...}& 8n\end{array}$

Step 3. Conclusion

From the above table, we can observe that the general terms will be $a_n=8n.$