Question

if an =2n - 1 then the common difference of that AP is​

Answer 1

Answer ---> Common difference = 2

Given---> aₙ = ( 2n - 1 )

To find---> Common difference of AP.

Solution---> ATQ,

aₙ = ( 2n - 1 )

Putting n = 1 , we get,

a₁ = 2 × 1 - 1

= 2 - 1

=> a₁ = 1

Putting n = 2 , we get,

=> a₂ = 2 × 2 - 1

=> a₂ = 4 - 1

=> a₂ = 3

Now , we have to find common difference, for which , we subtaract , first term from second term, so

Common difference = a₂ - a₁

=> d = 3 - 1

=> d = 2

Additional term--->

1) Formula for nth term of AP.

aₙ = a + ( n - 1 ) d

Where , a = first term

d = Common difference = a₂ - a₁

2) Formula of sum of n terms

Sₙ = ( n / 2 ) { 2a + ( n - 1 ) d }

Answer 2

an = 2n + 1

___________

Put n = 1

⇒a1 = 2(1) + 1

⇒a1 = 2 + 1

⇒a1 = 3

Put n = 2

⇒a2 = 2(2) +1

⇒a2 = 4 + 1

⇒a2 = 5

⇒d = a2 - a1

⇒d = 5 - 3

⇒d = 2