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 , …

Question

asked Jan 15, 2022 105k views

1 Answer

Tshirtman · Answer 1 · 2022-01-21T07:03:55+0000

Answer:

70

Explanation:

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

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

= 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.