How many terms of the sequence \( \sqrt{3}\), 3, \( 3 \sqrt{3}\),… must be taken to make the sum 39+ \( 13 \sqrt{3}\) ?

Asked by Sakshi | 1 year ago |  71

1 Answer

Solution :-

Given:

Sum of GP = \( 39 + 13\sqrt{3}\)

Where, a =\( \sqrt{3}\), r = \( 3\sqrt{3}\) = \( \sqrt{3}\), n = ?

By using the formula,

Sum of GP for n terms =

\( 39 + 13\sqrt{3} = \dfrac{\sqrt{3} (\sqrt{3}n – 1)}{(\sqrt{3} – 1)}\)

Let us simplify we get,

\( 39\sqrt{3} – 39 + 13(3) – 13\sqrt{3} = \sqrt{3} (\sqrt{3}n – 1)\)

\( 27\sqrt{3} = \sqrt{3}n+1\)

\( \sqrt{3}^6 \sqrt{3} = \sqrt{3}n+1\)

6+1 = n + 1

7 = n + 1

7 – 1 = n

6 = n

6 terms are required to make a sum of \( 39 + 13\sqrt{3}\)

Answered by Sakshi | 1 year ago

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