Q. 133.6( 5 Votes )
The sum of an infinite GP is 57, and the sum of their cubes is 9747. Find the GP.
Answer :
Let the first term Of G.P. be a, and common ratio be r.
∴
On cubing each term will become,
a3, a3r3, ….
∴This sum
a=57(1-r) put this in equation 2 we get
⇒ 
⇒ 
⇒ 19(1-2r+r2)=1+r+r2
⇒ 19r2-r2-38r-r+19-1=0
⇒ 18r2-39r+18=0
⇒ 6r2-13r+6=0
⇒ (2r-3)(3r-2)=0
⇒ r= 2/3, 3/2
But -1<r<1
⇒ r=2/3
Substitute this value of r in equation 1 we get
Thus the first term of G.P. is 19, and the common ratio is 2/3
∴G.P=19, 
19, 
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