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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

User Bain
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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.

User Chris Cap
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