Respuesta :

Addition can be defined as the process of adding two numbers. The correct option is D.

What is Addition?

Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.

The series will be as,

[tex]\dfrac{6}{1}-\dfrac{6}{3} + \dfrac{6}{9}-\dfrac{6}{27} + \dfrac{6}{81}-.....[/tex]

The sum of the first five terms of the series will be,

[tex]\rm Sum = \dfrac{6 \times 81}{1\times 81}-\dfrac{6\times 27}{3 \times 27} + \dfrac{6\times 9}{9\times 9}-\dfrac{6\times 3}{27\times 3} + \dfrac{6}{81}\\\\Sum = \dfrac{486-162+54-18+6}{81} \\\\Sum= \dfrac{366}{81}=\dfrac{122}{27}[/tex]

Hence, the correct option is D.

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ashishdwivedilVT

The sum of first five terms of the sequence is 122/27.

What is Sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Here, given sequence;

6 - 6/3 + 6/9 - 6/27+ .....

By observing we can say that this is a geometric sequence

So, sum of geometric series = a[tex](\frac{1-r^{n} }{1-r} )[/tex]

where, a is first term = 6

and r is common ratio = -1/3

and n is number of term = 5

Put the value in formula, we get

S₅ = 6[tex](\frac{1-(-1/3)^5}{1-(-1/3)} )[/tex]

S₅ = 6 [tex](\frac{(1+(1/243))}{1+(1/3)} )[/tex]

S₅ = (6 X 244)/(4 X 81)

S₅ = 122/27

Thus, the sum of first five terms of the sequence is 122/27.

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