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In a set of 4 terms first three terms are in gp and last three terms are in ap with a common difference 6.first term is equal to last term. Find first term

 
In a set of 4 terms first three terms are in gp and last three terms are in ap with a common difference 6.first term is equal to last term. Find first term

Grade:11

2 Answers

Ayush Mishra
44 Points
8 years ago
let the terms be a, ar,ar2 , b
 
  • as last three terms are in ap 
         2ar2=ar+b   ….. (i)
 
  • given then first and last terms are equal  => b=a
 
  • from (i)
=> 2ar2=ar+a
=> 2r2  – r – 1=0        
=> 2r2 -2r+r-1 = 0
=> r= 1 or r=
 
Ayush Mishra
44 Points
8 years ago
 r= 1 or r=(-1/2 )
 
since common difference is 6 , 
a= ar2 +6
 
 
if r=1
a=a+6  => 0=6   which is not possible so r cannot be 1
 
 
if r=-1/2
a=a/4 + 6
=> 3a/4 = 6
=> a=8
 
 
 
ans is  a=8

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