Question

Write an explicit formula for the following sequence. Find the twentieth term. 11, 12, 13, 14, 15, …

Answer 1

The arithmetic sequence is given by:

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

Where:

a1 = First term

d = Common difference

Using the data provided:

`\begin{gathered} a_1=11 \\ a_2=12=11+(2-1)d_{} \\ 12=11+d \\ d=12-11 \\ d=1 \end{gathered}`

Therefore, the explicit formula is:

`\begin{gathered} a_n=11+(n-1)1 \\ a_n=11+n-1 \\ a_n=n+10 \end{gathered}`

n = 20

`\begin{gathered} a_(20)=20+10 \\ a_(20)=30 \end{gathered}`

Answer:

`\begin{gathered} a_n=n+10 \\ a_(20)=30_{} \end{gathered}`