Question

I have no idea how to do this please help

Answer 1

Remember that

An explicit formula directly calculates the term in the sequence that you want

in this problem we have

5,8,11,14,...

so

a1=5

a2=8

a3=11

a4=14

a2-a1=8-5=3

a3-a2=11-8=3

a4-a3=14-11=3

the common difference d=3

An explicit formula is equal to

$a_n=a_1+d(n-1)$

we have

a1=5

d=3

substitute

$\begin{gathered} a_n=5+3(n-1) \\ a_n=5+3n-3 \\ a_n=2+3n \end{gathered}$

the answer is

an=2+3n