How many terms of the G.P. $$3, \dfrac{3}{2}, \dfrac{3}{4}, …$$ Be taken together to make $$\dfrac{3069}{512}$$ ?

Asked by Sakshi | 1 year ago |  84

##### Solution :-

Given:

Sum of G.P = $$\dfrac{ 3069}{512}$$

Where, a = 3, r =$$\dfrac{ \dfrac{3}{2}}{3} = \dfrac{1}{2}$$, n = ?

By using the formula,

Sum of GP for n terms =

$$\dfrac{ 3069}{512}$$$$\dfrac{ 3( 9\dfrac{1}{2})n – 1)}{ (\dfrac{1}{2} – 1)}$$

$$\dfrac{ 3069}{512}×3×2 =$$ $$1- (\dfrac{1}{2})^n$$

$$\dfrac{ 3069}{3072}– 1=$$  $$– (\dfrac{1}{2})^n$$

$$\dfrac{ (3069 – 3072)}{3072} = – (\dfrac{1}{2})^n$$

10 = n

10 terms are required to make $$\dfrac{ 3069}{512}$$

Answered by Sakshi | 1 year ago

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