Arithmetic and Geometric Progressions

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AP: Sum up to 'n' Terms

    Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?

 

  • Correct Answer
    Choice A.

Detailed Solution

The sum of the first 25 terms, S25 = 525
The sum of the next 25 terms, K25 = sum of next 25 terms = 725
a26 = a1 + 25d
a27 = a2 + 25d

K25 = a26 + a27 + ...... + a50
Or K25 = a1 + 25d + a2 + 25d + ...... + a25 + 25d
Or K25 = a1 + a2 + ...... + a25 + 25(25d)

Or K25 = S25 + 25(25d)
i.e., 725 = 525 + 25 x 25d
200 = 25 x 25d
8 = 25d
d =

Correct Answer:



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More questions from Progressions

  1. Counting and Progressions
  2. Common Ratio
  3. Common Difference
  4. Sum up to 'n' Terms
  5. AP Puzzle
  6. GP Logical Puzzle
With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.