Question

Can you help me with this.

Answer 1

We have the following arithmetic sequence:

`2,5,8,11,\ldots`

Now, the general n-term of this sequence can be written in the following way:

`a_n=2+(n-1)\cdot3`

where n takes the following values:

`n=1,2,3,\ldots`

We see that this general term reproduces the sequence about:

`\begin{gathered} a_1=2+(1-1)\cdot3=2+0=2 \\ a_2=2+(2-1)\cdot3=2+3=5 \\ a_3=2+(3-1)\cdot3=2+6=8 \\ a_4=2+(4-1)\cdot3=2+9=11 \\ \ldots \end{gathered}`

We can find the 13th term of sequence simply replacing n by 13 in the general formula above, we get:

`\begin{gathered} n=13\rightarrow a_n=2+(n-1)\cdot3 \\ \rightarrow a_(13)=2+(13-1)\cdot3=2+36=38 \end{gathered}`

Answer

The 13th term of the sequence is:

`a_(13)=38`