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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 ​ , ...

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Answer:

70

Step-by-step explanation:

[tex]a_1[/tex] = First term = [tex]\dfrac{1}{3}[/tex]

[tex]d[/tex] = Common difference = [tex]\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}[/tex]

[tex]n[/tex] = Number of terms = 20

Sum of arithmetic progression is given by

[tex]S=\dfrac{n}{2}[2a_1+(n-1)d]\\\Rightarrow S=\dfrac{20}{2}\times (2\times \dfrac{1}{3}+(20-1)\dfrac{1}{3})\\\Rightarrow S=70[/tex]

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

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