Question

Given the first term, f(1) = 3 and the common difference of 4, find the first five terms.A. 3,5,7,9,11B. 3, 12, 36, 108, 324C. 3, 7, 11, 15, 19D. 3, 4, 5, 6, 7

Answer 1

If the sequence has a common difference of 4, this means that:

$f(n+1)-f(n)=4\text{ for every n}$

We can use that to find f(2), f(3), etc...

$\begin{gathered} f(2)-f(1)=4 \\ \Rightarrow f(2)=4+f(1) \end{gathered}$

Substitute f(1)=3:

$f(2)=4+3=7$

The next term will be given by:

$\begin{gathered} f(3)=4+f(2) \\ \Rightarrow \\ f(3)=4+7=11 \end{gathered}$

By adding 4 to the previous term, it follows that f(4)=15, f(5)=19, and so on.

The sequence 3, 7, 11, 15, 19 appears in the option C.