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Show that the sum of all terms of an A.P...

Show that the sum of all terms of an A.P whose first term is a, the second term is b and the last term is b and the last term is c is equal to `((a+c)(b+c-2a))/(2(b-a))`

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AGRAWAL PUBLICATION-ARITHMETIC PROGRESSIONS-EXAMPLE
  1. How many numbers lie between 10 and 300, which when divided by 4 leave...

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  2. Find the sum of the two middle most terms of the AP: -4/3, -1,-2/3, …....

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  3. Show that the sum of all terms of an A.P whose first term is a, the se...

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  4. The first term of an ap is -5 and the last term is 45. If the sum of t...

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  5. If Sndenotes the sum of first n terms of an AP, prove that S(12) = ...

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  6. If the sum of the first 6 terms of an AP is 36 and that of the fist 16...

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  7. The sum of the first n terms of an AP whose first term is 8 and the co...

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  8. If m^(th) term of an A.P. is 1/n and n^(th) term is 1/m. Find the sum ...

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  9. Find the sum of n terms of the series (4 -1/n) + (4 - 2/n) + (4- 3/n) ...

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  10. For what value of n are the n^(th) terms of two A.P's 63,65,67, ….. An...

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  11. Find the sum of the first 40 positive integers which give a remainder ...

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  12. Divide 56 in four parts in A.P. such that the ratio of the product of ...

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  13. If the sum of the first 7 terms of an A.P. is 49 and that of its first...

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  14. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  15. How many terms of an A.P. 9,17,25,….m must to be taken to give a sum o...

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  16. Among the natural numbers 1 to 49, find a number x, such that the sum ...

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  17. The 14^(th) term of an AP is twice 8^(th) term. If its 6^(th) term is ...

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  18. The digits of a positive number of three digits are in A.P and their s...

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  19. The digits of a positive number of three digits are in A.P and their s...

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  20. Find the sum of first 24 terms of an A.P. whose n^(th) term is given b...

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