Question

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

7, 14, 21, 28, 35, …

Short answer

The general term for the sequence whose first five terms are 7, 14, 21, 28, 35, … is$a_n=7n.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thefirstfivetermsofthesequenceare}\\ 7,14,21,28,35,\dots \\ \text{Wehavetofindthegeneraltermforthesequence.}\end{array}$

Step 2. Observing the pattern

Now,

$\begin{array}{cccccccc}n:& 1& 2& 3& 4& 5& \mathrm{...}& n\\ \text{Terms}& 7& 14& 21& 28& 35& \mathrm{...}& \\ \text{Pattern}& 7\cdot 1& 7\cdot 2& 7\cdot 3& 7\cdot 4& 7\cdot 5& \mathrm{...}& 7\cdot n\end{array}$

Step 3. Conclusion

From the above table we can observe that the general terms will be$a_n=7n.$