Question

what is the 20th term of the following arithmetic sequence?

Answer 1

\[\frac{ 1 }{ 2 }, 1, \frac{ 3 }{ 2 }, 2\]

Answer 2

@zepdrix

Answer 3

\[\Large a_1=\frac{1}{2}, \qquad a_2=1\]
If we subtract,\[\Large a_2-a_1=1-\frac{1}{2}\]Let's call this value k.\[\Large k=\frac{1}{2}\]
This is the common difference between each term.

Answer 4

The nth term is given by,\[\Large a_n=a_1+(n-1)k\]

Answer 5

\[\Large a_{20}=?\]Can you figure this one out? :)
Plug in 20 for all of your n's.
And plug in the first value for a_1.

Answer 6

a20 = 30?

Answer 7

Hmm let's fill in the pieces.\[\Large a_\color{royalblue}{n}=\color{orangered}{a_1}+(\color{royalblue}{n}-1)\color{green}{k}\]

\[\Large \color{royalblue}{n=20},\qquad\qquad \color{orangered}{a_1=\frac{1}{2}},\qquad\qquad \color{green}{k=\frac{1}{2}}\]

Answer 8

\[\Large a_\color{royalblue}{20}=\color{orangered}{\frac{1}{2}}+(\color{royalblue}{20}-1)\color{green}{\frac{1}{2}}\]

Answer 9

Try to solve that! :D