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If a ,b ,c are in A.P., prove that ...

If `a ,b ,c` are in A.P., prove that `1/(b c),1/(c a),1/(a b),` is also in A.P.

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If we divide the numbers in AP with the same number, the resulting numbers will also be in AP.

Divide by `abc. a/abc, b/abc, c/abc` are in AP. So `1/bc, 1/ac, 1/ab` are in AP.
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If (b+c-a)/a ,(b+c-a)/b ,(a+b-c)/c , are in A.P., prove that 1/a ,1/b ...

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  2. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a...

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  3. If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is al...

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  4. If a^2,b^2,c^2 are in A.P., then prove that the following are also in...

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  5. Two cars start together in the same direction from the same place. The...

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  6. Find an A.P. in which the sum of any number of terms is always three ...

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  7. If log2,log(2^x-1),log(2^x+3) are in A.P., write the value of xdot

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  8. The sums of first n terms of two A.P. ' s are in hte ratio (7n+2):(n+4...

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  9. Give first 3 terms of the sequence defined by an=n/(n^2+1)dot

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  10. First term of a sequence is 1 and (n+1)th term is obtained by adding (...

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  11. 1,4,7,10,is an A.P. whose first term is 1 and the common difference is...

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  12. 11, 7, 3, -1 is an A.P. whose first term is 11 and the common diffe...

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  13. The nth term of a sequence is 3n-2 is the sequence an A.P.? If so, fin...

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  14. If the nth term an\ of a sequence is given by an=n^2-n+1 write down i...

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  15. A sequence is defined by an=n^3-6n^2+11 n-6. Show that the first three...

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  16. Find the first four terms of the sequence defined by a1=3\ a n d\ an=3...

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  17. Write the first five terms in each of the following sequence: a1=1,\ a...

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  18. Write the first five terms in each of the following sequence: a1=1=\ a...

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  19. Write the first five terms in each of the following sequence: a1=a2=2,...

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  20. The Fibonacci sequence is defined by a1=1=a2,\ an=a(n-1)+a(n-2) for n ...

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