Question

The product of three terms of a GP is 512. If 8 is added to the first term and 6 to the second term, find the new terms form an AP

Answer 1

Lets take the first term of the G.P. to be a and common ratio to be r. then first three terms of the G.P. => a,ar and ar^2 . if we multiply the three terms ,we get a^3r^3 =512(given) .on applying cube root on both sides we get ar=8. So the other terms can be written as 8/r ,8, 8r . it is said that if we add 8 to first term and 6 to second term it forms a A.P.
First term is 8/r+ 8,Second term is 8+6=14 and third term is 8r . In an A.P. ,the second term when multiply by 2 = sum of first term and third term
=> 2(14) = 8/r+8+8r

=> 28-8 =8/r +8r

=> 20= 8/r +8r

multiply each term by r , we get

=>20r= 8 + 8r^2

=>2r^2-5r+2=0

=>2r^2-4r-r+2=0=>2r(r-2)-1(r-2)

=>(2r-1)(r-2)

=> so we get r=1/2 or 2 => The terms of the G.P.
are 8/(1/2),8,8(1/2)=> 16,8,4 .Hope it helps you...

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Answer 2

16,8 and 4 are the correct answer s