# 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), ...

#### 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?

#### APPEARS IN

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