Question

Find a general term for the sequence whose first five terms are shown. 4, 8, 12, 16, 20, …

Short answer

The general term for the given sequence is$a_n=3n.$

Step-by-step solution

Step 1. Given information

The first five terms are 4, 8, 12, 16, 20, …

We have to find the general term for the given sequence.

Step 2. Calculating the pattern

$\begin{array}{llllllll}n& 1& 2& 3& 4& 5& \mathrm{...}& n\\ \text{Terms}& 3& 6& 9& 12& 15& \mathrm{...}& \\ \text{Pattern}& 3\left(1\right)& 3\left(2\right)& 3\left(3\right)& 3\left(4\right)& 3\left(5\right)& \mathrm{...}& 3\left(n\right)\end{array}$

Step 3. Conclusion

From the above table, we can observe that all the numbers are multiple of 3.

Therefore, the general term for the given sequence is$a_n=3n.$