Question

Find a general term for the sequence whose first five terms are shown. 5, 10, 15, 20, 25, …

Short answer

The general term for the given sequence is$a_n=5n.$

Step-by-step solution

Step 1, Given information

The first five terms of the sequence are 5, 10, 15, 20, 25,...

Step 2. Observing the pattern

$\begin{array}{llllllll}n& 1& 2& 3& 4& 5& \mathrm{...}& n\\ \text{Terms}& 5& 10& 15& 20& 25& \mathrm{...}& \\ \text{Pattern}& 5\left(1\right)& 5\left(2\right)& 5\left(3\right)& 5\left(4\right)& 5\left(5\right)& \mathrm{...}& 5\left(n\right)\end{array}$

Step 3. Conclusion

From the above table, we can observe that all the numbers are multiple of 5.

Therefore, the general term for the given sequence is $a_n=5n.$