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deepaksoni
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Asked: 2021-05-27T11:10:32+05:30 In:

Problem 5: Prove that no matter what the real numbers a and b are, the sequence with nth term a + nb is always an A.P. What is the common difference?

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This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.3

We have to prove that for all real numbers a, b the sequence with nth term  a+nb is always an AP. Also we have to find the common difference.

CBSE DHANPAT RAI publications
Class:- 10th
Understanding CBSE Mathematics
Question 5

arithmetic progressionsclass 10thrd sharma
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      Solution: 

      an = a + nb

      Let n= 1, 2, 3, 4, 5, ……….

      a1 = a + b

      a2 = a + 2b

      a3 = a + 3b

      a4 = a + 4b

      a5 = a + 5b

      Now,

      a2 – a1 = (a + 2b) – (a + b) = b

      a3 – a2 = (a + 3b ) – (a + 2b) = b

      a4 – a1 = (a + 4b) – (a + 3b) = b

      a5 – a4 = (a + 5b) – (a + 4b) = b

      Hence, proved

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