The sum of five terms is 208/375 or the value of S(4) is 208/375 option third is correct.
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
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We have:
[tex]\rm \sum_{n=1}^\infty\dfrac{2}{3}(\dfrac{-1}{5})^{n-1}[/tex]
Plug n = 1
We will get the first term:
a = 2/3
The sum of the terms of a geometric sequence is given by the formula:
[tex]\rm S_n = \dfrac{a(1-r^n)}{1-r}[/tex]
r = -1/5
[tex]\rm S_4 = \dfrac{a(1-(-1/5)^4)}{1-(-1/5)}[/tex]
After solving:
S(4) = 208/375
Thus, the sum of five terms is 208/375 or the value of S(4) is 208/375 option third is correct.
Learn more about the sequence here:
brainly.com/question/21961097
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