Calculate First Five Terms: Sequence Formula an=3n+1

In order to determine the first five terms in the sequence simply insert their positions into the given formula as shown below:

$a_n=3n+1$

We want to calculate the values of the terms:

$a_1,\hspace{4pt}a_2,\hspace{4pt}a_3,\hspace{4pt}a_4,\hspace{4pt}a_5$

Let's start with the first term in the sequence,

$a_n=3n+1$

We need to insert the position of whichever term that we want to find.

In this case we want to find the first term so we'll substitute as shown below:

$n=1$

Proceed to calculate:

$a_{\underline{n}}= 3\underline{n}+1 \\ n=\underline{1}\\ \downarrow\\ a_{\underline{1}}=3\cdot\underline{1}+1=4$

When we substituted the position in question in the place of n : the substitution is shown with an underline (as shown above),

Repeat this exact action for all the requested terms in the sequence, meaning for the second through fifth terms:

$a_{\underline{2}}=3\cdot\underline{2}+1=7 \\ a_{\underline{3}}=3\cdot\underline{3}+1=10 \\ a_{\underline{4}}=3\cdot\underline{4}+1=13 \\ a_{\underline{5}}=3\cdot\underline{5}+1=16 \\$For the second term $a_2$ we substituted:$n=2$ in to the formula:

$a_n=3n+1$

For the third term $a_3$ we again substituted:$n=3$ and so on for the rest of the requested terms,

To summarize, we determined that the first five terms:

$a_1,\hspace{4pt}a_2,\hspace{4pt}a_3,\hspace{4pt}a_4,\hspace{4pt}a_5$

in the given sequence, are:

$4,\hspace{4pt}7,\hspace{4pt}10,\hspace{4pt}13,\hspace{4pt}16$

Therefore, the correct answer is answer A.