Arithmetic and Geometric Progressions

You are here: Home  CAT Questionbank   CAT Quant  AP, GP  Question 4

AP: Common Difference

    Let the nth term of AP be defined as tn, and sum up to 'n' terms be defined as Sn. If |t8| = |t16| and t3 is not equal to t7, what is S23?
    1. 23(t16 - t8)
    2. 0
    3. 23t11
    4. Cannot be determined


  • Correct Answer
    Choice B. 0

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

Detailed Solution

|t8|=|t16|. This can happen under two scenarios t8 = t16 or t8 = – t16.

If t8 = t16, the common difference would be 0 suggesting that t3 would be equal to t7. However, we know t3 is not equal to t7, so the common difference cannot be zero.

This tells us that t8 = – t16 Or, t8 + t16 = 0.

If t8 + t16 = 0, then t12 = 0. t12 = t8 + 4d, and t16 – 4d So, t12 =

  • . For any two terms in an AP, the mean is the term right in between them. So, t12 is the arithmetic mean of t8 and t16.

    So, t12 = 0.
    Now, S23 = 23 × t12. We know that average of n terms in an A.P. is the middle term. This implies that sum of n terms in an A.P., is n times the middle term. So, S23 = 0. Correct Answer: zero.

    Our Online Course, Now on Google Playstore!

    2IIM's App

    Fully Functional Course on Mobile

    All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

    Cache Content for Offline Viewing

    Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

    Get it on Google Play

    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.