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The 4th and 7th terms of a G.P. are 18 a...

The 4th and 7th terms of a G.P. are 18 and 486 respectively. Find the G.P.

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Let first term and common ratio of G.P. be 'a' and 'r' respectively.
`therefore" "T_(4)=acdotr^(3)=18" ...(1)"`
`"and "T_(7)=acdotr^(6)=486" ...(2)"`
Divide eq. (2) by eq. (1)
`(ar^(6))/(ar^(3))=(486)/(18)`
`rArr" "r^(3)=27=3^(3)`
`rArr" "r=3`
Put this value in eq. (1)
`a(3)^(3)=18`
`rArr" "a=(2)/(3)`
`therefore" "G.P.=a,ar,ar^(2),...`
`=(2)/(3),2,6,...`
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NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Miscellaneous Exercise
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  13. The sum of the first four terms of an A.P. is 56. The sum of the last ...

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  17. If a (1/b+1/c),b(1/c+1/a),c(1/a+1/b)are in A.P., prove that a, b, c a...

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  19. If a\ a n d\ b are the roots of x^2-3x+p=0\ a n d\ c ,\ d are the root...

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  20. The ratio of the A.M. and G.M. of two positive numbers a and b, is m ...

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  21. If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/eare in A....

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