Question

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

−3, −2, −1, 0, 1, …

Short answer

The general term for the sequence whose first five terms are −3, −2, −1, 0, 1, … is$a_n=n-4.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thefirstfivetermsofthesequenceare}\\ -3,-2,-1,0,1,\dots \\ \text{Wehavetofindthegeneraltermforthesequence.}\end{array}$

Step 2. Observing the pattern

Now,

$\begin{array}{cccccccc}n:& 1& 2& 3& 4& 5& \mathrm{...}& n\\ \text{Terms}& -3& -2& -1& 0& 1& \mathrm{...}& \\ \text{Pattern}& 1-4& 2-4& 3-4& 4-4& 5-4& \mathrm{...}& n-4\end{array}$

Step 3. Conclusion

From the above table we can observe that the general terms will be$a_n=n-4.$