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Find an A.P. in which the sum of any num...

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

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AP-.a,d
`n/2[2a+(n-1)d]=3n^2`
`2a+(n-1)d=6n`
`2a+(d-6)n-d=0`
`d-6=0`
`d=6`
`2a-d=0`
`2a=6`
...
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If a^2,b^2,c^2 are in A.P., then prove that the following are also in...

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

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

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

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

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

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

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  8. 1,4,7,10,is an A.P. whose first term is 1 and the common difference is...

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  9. 11, 7, 3, -1 is an A.P. whose first term is 11 and the common diffe...

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

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

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

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

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

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

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

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

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  18. Show that each of the following sequences is an A.P. Also, find the ...

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  19. Show that each of the following sequences is an A.P. Also, find the ...

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  20. The nth term of a sequence is given by an=2n^2+n+1. Show that it is no...

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