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Insert two number between 3 and 81 so th...

Insert two number between 3 and 81 so that the resulting sequence is G.P.

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Let required numbers be a and b . Then, the sequence 3,a,b 81 will be in G.P.
`a_(4)=81`
`implies 3r^(3)=81implies r^(3)=27`
`implies r=3`
`:. A=3xxr=3xx3=9`
`b=a_(1)xxr^(2)=3xx9=27`
Therefore, number and 9 and 27
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NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Exercise 9.3
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  2. The sum of first three terms of a G.P is 16 and the sum of the next th...

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  3. Given a G.P with a=729 and 7th term 64,determine S(7).

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  4. Find a G.P. for which sum of the first two terms is -4 and the fifth ...

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  5. If the 4th, 10th and 16 th terms of a G.P. are x, y and z, respectivel...

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  6. Find the sum to n terms of the sequence 8,88,888,8888,……

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  7. Find the sum of the product of the corresponding terms of the sequence...

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  8. Show that the products of the corresponding terms of the sequence a,...

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  9. Find four numbers forming a geometric progression in which the third t...

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  10. If the pth, qth and rth terms of a G.P. are a,b and c, respectively. ...

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  11. If the first and the nth term of a G.P. are a and b, respectively, and...

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  12. Show that the ratio of the sum of first n terms of a G.P. to the sum o...

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  13. If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b...

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  14. Insert two number between 3 and 81 so that the resulting sequence i...

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  15. 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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  16. The sum of two numbers is 6 times their geometric means, show that nu...

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  17. If A and G be A.M. and GM., respectively between two positive numbers...

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  18. The number of bacteria in a certain culture doubles every hour. If ...

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

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  20. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respe...

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