Question

What is the sum of the first 20 terms of the arithmetic sequence shown? \displaystyle \frac{1}{3} 3 1 ​ , \displaystyle \frac{2}{3} 3 2 ​ , 1, \displaystyle \frac{4}{3} 3 4 ​ , \displaystyle \frac{5}{3} 3 5 ​ , ...

Answer 1

70

Explanation:

`a_1` = First term =
`(1)/(3)`

`d` = Common difference =
`(2)/(3)-(1)/(3)=(1)/(3)`

`n` = Number of terms = 20

Sum of arithmetic progression is given by

`S=(n)/(2)[2a_1+(n-1)d]\\\Rightarrow S=(20)/(2)* (2* (1)/(3)+(20-1)(1)/(3))\\\Rightarrow S=70`

The sum of the first 20 terms of the arithmetic sequence is 70.