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

Let's find the first five terms in the sequence by substituting their positions in the given general term formula:

$a_n=3n+1$

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,

meaning in the given general term formula:

$a_n=3n+1$

We need to substitute the position (of the requested term in the sequence),

We want to find the first term so we'll substitute:

$n=1$

Let's perform this:

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

When we substituted in place of n the position (of the requested term in the sequence): 1, the substitution is shown with an underline in the expression above,

We'll repeat this action identically for all the requested terms in the sequence, meaning for the second through fifth terms:

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

$a_n=3n+1$

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

To summarize, we found 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.