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Home » How many terms of the series 2 + 6 + 18 + …. Must be taken to make the sum equal to 728?
How many terms of the series 2 + 6 + 18 + …. Must be taken to make the sum equal to 728?
CBSE | Class 11 | Exercise 20.3 | Geometric Progressions | Maths | RD Sharma
How many terms of the series 2 + 6 + 18 + …. Must be taken to make the sum equal to 728?

Solution:

Given that,
The sum of GP =728
Where, a=2, r=6 / 2=3, n=?
Using the formula,
The sum of GP for n terms =a\left(r^{n}-1\right) /(r-1)
\begin{array}{l} 728=2\left(3^{n}-1\right) /(3-1) \\ 728=2\left(3^{n}-1\right) / 2 \\ 728=3^{n}-1 \\ 729=3^{n} \\ 3^{6}=3^{n} \\ 6=n \end{array}
As a result, 6 terms are required to make a sum equal to 728

i

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