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We are given two G.P.'s, one with the fi...

We are given two G.P.'s, one with the first term 'a' and common ratio ‘r’ and the other with first term ‘b’ and common ratio ‘s’. Show that the sequence formed by the product of corresponding terms is a G.P. Find its first term and the common ratio. Show also that the sequence formed by the quotient of corresponding terms is G.P. Find its first term and common ratio.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If the mth, nth and pth terms of a G.P. form three consecutive terms o...

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  2. If x,y,z are in G.P. and a^x= b^y=c^z, prove that logb a. logb c=1.

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  3. We are given two G.P.'s, one with the first term 'a' and common ratio ...

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  4. If Sn represents the sum of n terms of a G.P. whose first term and com...

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  5. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  6. Find the derivative of the following y=x+1/x+sinx

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  7. The sum of the first three consecutive terms of G.P. is 13 and the sum...

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  8. If 1/(a+b)+1/(b+c)=1/b, prove that a, b, c are in G.P.

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  9. 150 workers were engaged to finish a job in a certain number of days. ...

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  10. The height of a plant at a certain date is 1.6 metre. If it increases ...

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  11. If |x|<1 and |y|<1, find the sum to infinity of the series : (x+y)+(x^...

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  12. A manufacturer reckons that the value of a machine, which costs him Rs...

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  13. Prove the following by using the principle of mathematical induction f...

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  14. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

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  15. Find the sum of n terms\ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+do...

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  16. Obtain the sum of the series : 1/1.4+1/4.7+1/7.10 + .......... to n t...

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  17. Find the sum of n terms of the series (1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)...

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  18. Show that : (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. ...

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  19. What will Rs 500 amounts to in 10 years after its deposit in a bank wh...

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  20. A man deposited ₹ 10,000 in a bank at the rate of 5% simple interest a...

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