If 64,27,36 are the Pth,Qth and Rth terms of a G.P., then
P+2Q is equal to
  (a) R      (b) 2R     (c) 3R      (d) 4R

Asked by aliencpr31 | 31st Jul, 2019, 10:55: AM

Expert Answer:

We know that,
 
nth term of a G.P is given by,
 
tn = arn-1
 
According to the question,
a. rP-1 = 64   ... (1)
a. rQ-1 = 27  ... (2)
a. rR-1 = 36  ... (3)
 
To find: P + 2Q = ?
 
Hint :
P is having a coefficient 1 , Q is having a coefficient 2 and from the options
if we take 3R , so the cofficient of R is 3.

begin mathsize 16px style rightwards double arrow fraction numerator 64 space cross times open parentheses 27 close parentheses squared over denominator open parentheses 36 close parentheses cubed end fraction space equals space 1
From space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis comma space we space get

fraction numerator open parentheses straight a. straight r to the power of straight P minus 1 end exponent close parentheses open parentheses straight a. straight r to the power of straight Q minus 1 end exponent close parentheses squared over denominator open parentheses straight a. straight r to the power of straight R minus 1 end exponent close parentheses cubed end fraction space equals space 1
rightwards double arrow straight r to the power of straight P minus 1 space plus space 2 straight Q space minus space 2 space minus space 3 straight R space plus space 3 end exponent space equals space straight r to the power of 0
rightwards double arrow straight P minus 1 space plus space 2 straight Q space minus space 2 space minus space 3 straight R space plus space 3 space equals space 0
rightwards double arrow straight P space plus space 2 straight Q space equals space 3 straight R

Correct space Option colon space left parenthesis straight C right parenthesis end style
 
 
 
 
 


 
 

Answered by Yasmeen Khan | 31st Jul, 2019, 02:28: PM

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