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Problem 6: Justify whether it is true to say that the sequence, having following nth term is an A.P. (iii) an = 1 + n + n² .

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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.2
In this question we have been given the sequence and we have to find out that it is an AP or not.

CBSE DHANPAT RAI publication
Understanding CBSE Mathematics
Question 6(iii)

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1 Answer

  1. Solution:

    Now putting n = 1, 2, 3 we get,

    a1 = 1 + 1 + 1.1 = 3

    a2 = 1 + 2 + 2.2 = 7

    a3 = 1 + 3 + 3.3 = 13

    We can see that,

    a2 – a1 = 7 – (3) = 4

    a3 – a2 = 13 – (7) = 6

    Since, the successive difference of list is not the same

    Hence, the given sequence is not in A.P

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