Question

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

6, 7, 8, 9, 10, …

Short answer

The general term for the sequence whose first five terms are 6, 7, 8, 9, 10, … is$a_n=n+5.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thefirstfivetermsofthesequenceare}\\ 6,7,8,9,10,\dots \\ \text{Wehavetofindthegeneraltermforthesequence.}\end{array}$

Step 2. Observing the pattern

Now,

$\begin{array}{cccccccc}n:& 1& 2& 3& 4& 5& \mathrm{...}& n\\ \text{Terms}& 6& 7& 8& 9& 10& \mathrm{...}& \\ \text{Pattern}& 1+5& 2+5& 3+5& 4+5& 5+5& \mathrm{...}& n+5\end{array}$

Step 3. Conclusion

From the above table, we can observe that the general terms will be$a_n=n+5.$