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The fourth power of common difference of...

The fourth power of common difference of an arithmetic progression with integer entries is added to the product of any four consecutive terms of it. Prove that the resulting sum is the square of an integer.

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. The nth term of a sequence is given by an=2n+7. Show that it is an A.P...

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  2. The product of three numbers in A.P. is 224, and the largest number is...

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  3. The fourth power of common difference of an arithmetic progression wit...

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  4. The sum of three terms of an A.P. is 21 and the product of the first ...

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  5. The internal angles of quadrilateral are in A.P. and their common diff...

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  6. Find the sum of all natural between 250 and 1000 which are exactly ...

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  7. Find the sum of first 20 terms of an A.P., in which 3r d terms in 7 an...

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  8. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  9. The sums of n terms of three arithmetical progressions are S1, S2and ...

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  10. If in an A.P. the sum of m terms is equal of n and the sum of n ter...

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  11. The first , second and the last terms of an A.P. are a ,b , c respect...

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  12. If (3+5+7+ u p tont e r m s)/(5+8+11+ u p to10t e r m s)=7, then find...

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  13. In a factory, 150 workers were engaged to finish a piece of work in a ...

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  14. Prove that the sum of n arithmetic means between two numbers in n ti...

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  15. If a ,b ,c are in A.P., then prove that: (a – c)^2 = 4(b^2 – ac).

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  16. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

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  17. If n arithemetic means are inserted between 20 and 80 such that the ra...

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  18. Along a road lie an odd number of stones placed at intervals of 10 met...

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  19. A carpenter was hired to build 192 window frames. The first day he mad...

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  20. In a potato race 20 potatoes are placed in a line at intervals of 4m e...

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