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The sum of an infinite G.P. is 57 and th...

The sum of an infinite G.P. is 57 and the sum of their cubes is `9457 ,` find the G.P.

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To solve the problem, we need to find the terms of an infinite geometric progression (G.P.) given that the sum of the infinite G.P. is 57 and the sum of their cubes is 9457. ### Step 1: Set Up the Equations Let the first term of the G.P. be \( A \) and the common ratio be \( r \). The formula for the sum of an infinite G.P. is given by: \[ S = \frac{A}{1 - r} ...
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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Find the sum of an infinitely decreasing G.P. whose first term is equa...

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  2. If x=sum(n=0)^oocos^(2n)theta,y=sum(n=0)^oosin^(2n)varphi,z=sum(n=0)^o...

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  3. The sum of an infinite G.P. is 57 and the sum of their cubes is 9457 ,...

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  4. Which is the rational number having the decimal expansion 0.3 bar( 56)...

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  5. A square is drawn by joining the mid-points of the sides of a square. ...

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  6. After striking a floor a certain ball rebounds (4/5)^(t h) of the heig...

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  7. Sum the following geometric series to infinity: 1/2+1/(3^3)+1/(2^3)+1/...

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  8. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, ...

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  9. If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove...

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  10. If A=1+r^a+r^(2a)+ to oo and B=1+r^b+r^(2b)+oo , prove that r=((A-1)/A...

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  11. Prove that the product n geometric means between two quantities is equ...

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  12. If a ,b ,c ,d are four distinct positive numbers in G.P. then A. a +...

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  13. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n)may be the geo...

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  14. Insert 5 geometric means between 576 and 9.

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  15. Let x be the arithmetic mean and y ,z be tow geometric means between a...

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  16. Find two positive numbers whose difference is 12 an whose A.M. exce...

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  17. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

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  18. If a is the A.M. of b and c and the two geometric means are G1 and G2...

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  19. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

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  20. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

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