Question

First term 'a' and common ratio 'r' .if the sum is 4 and second term is 3/4 then

Answer 1

★ GEOMETRIC PROGRESSION ★

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Please always try to post complete question without some discrete information being left out as this tends to be an invalid question on brainly.in and can be deleted. I would prefer to complete the question as follows on the basis of most frequently matching questions asked and available:

Consider an infinite geometric series with first term and common ratio r. If its sum is 4 and the second term is 3/4, then : 

(A) a=4/7, r=3/7               
(B) a =2, r = 3/8 
(C) a = 3/2, r = 1/2                                
(D) a = 3, r = 1/4  

Hope this is the correct assumption. Just compare with your original text source and let me know if this assumption is right or wrong so that I can make some required changes if needed.

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Given, $ar = \frac{3}{4}$ 
And, $\frac{a}{1-r} = 4$

So, $a = \frac{3}{4r}$

Substuting this in $\frac{a}{1-r} = 4$,
We get, $\frac{3}{r(1-r)} = 16$ 

⇒ $16 r^{2} -16r +3 = 0$

Thus, $r = \frac{1}{4}$ 
Or, $r = \frac{3}{4}$

∴ Option (D) is the answer with a = 3 and r = $\frac{1}{4}$.

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