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If a, b, c are in A.P., b, c, d are in G...

If a, b, c are in A.P., b, c, d are in G.P. and `1/c ,1/d ,1/e`are in A.P. prove that a, c, e are in G.P.

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As a,b and c are in A.P.
`a-b = b-c`
`a/b - 1 = 1-c/b->(1)`
As, b,c and d are in G.P.
`bd = c^2->(2)`
As, 1/c,1/d,1/e are in A.P.
`1/d-1/e = 1/e-1/d`
...
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NCERT-SEQUENCES AND SERIES-MISCELLANEOUS EXERCISE
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  2. Find the sum of the following series up to n terms: (i) 5 + 55 + 555 +...

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  3. 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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  8. A G.P. consists of an even number of terms. If the sum of all the ter...

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  11. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  12. The p^(t h),q^(t h)and r^(t h)terms of an A.P. are a, b, c, respectiv...

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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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  14. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0),then show that...

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  15. The sum of three numbers m GP is 56. If we subtract 1.7,21 from these...

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

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  18. Show that the sum of (m+n)^(t h)and (m-n)^(t h)terms of an A.P. is eq...

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  19. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

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  20. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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