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Which the Following Sequences is Arithmetic Progressions. for is Arithmetic Progression, Find Out Common Difference. a + B, (A + 1) + B, (A + 1) + (B + 1), (A + 2) + (B + 1), (A + 2) + (B + 2), ... - Mathematics

Sum

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...

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Solution

a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ... 

Here,

First term (a) = + b

`a_1 = ( a + 1) + b`

`a_1 = ( a + 1) + (b +1)`

Now, for the given to sequence to be an A.P,

Common difference (d)  ` = a_1 - a = a_2 -a_1`

Here,

`a_1 -a = a + 1 + b - a- b`

             = 1

Also,

`a_2 - a_1 = a+1+b+1-a-1-b`

               = 1

Since  `a_1 - a = a_2 -a_1`

Hence, the given sequence is an A.P and its common difference is  d = 1

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.3 | Q 6.1 | Page 11
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