Question

in an arithmetic progression if an=2n+1then the common difference of the given progression is
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Answer 1

Given : In an arithmetic progression aₙ  =  2n + 1

To find :  the common difference of the given progression

Solution:

aₙ  =  2n + 1

aₙ₊₁ = 2(n+1) + 1  = 2n + 2 + 1

=> aₙ₊₁ = 2n + 2 + 1

=> aₙ₊₁ = 2n + 3

Common Difference of an AP

= aₙ₊₁   - aₙ

= 2n + 3  - (2n + 1)

= 2n + 3 - 2n -  1

= 3 - 1

= 2

Hence Common Difference   of AP  = 2

Another way n = 1

=> a₁ = 2(1) + 1 = 3

    a₂ = 2(2) + 1 = 5

Common difference =  

a₂ = a₁ + d

=> 5 = 3 + d

=> d = 2

Hence AP =  3 , 5 , 7  , 9 ,,,,,,,,,,,,,,,,,,,,,

common difference of the given progression =   2

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