Question

1, 1+root2, 1+2root2, 1+3root2,..... Is this an arithmetic sequence? Why?

Answer 1

Answer:

in an A.P , a₂ - a₁ =d1, a₃ - a₂ = d2

d1 = d2

here 1 +2√2 - ( 1+√2) = 1+2√2-1-√2 =

√2 = d1

similarly 1+3√2 - (1+2√2) =

1+3√2-1-2√2 =

√2 = d2

d1 = d2

here d = √2

hence the sequence is in A.P

Answer 2

Answer:

The common differences are equal.

Step-by-step explanation:

The given sequence is in AP.

This is because, the common difference is same between 2 terms of the given AP.

Common difference = a₂-a₁

= 1+√2 - 1

=√2

Common difference = a₃-a₂

=1+2√2 - 1-√2

=√2

As, common difference is same, it is proved that the given sequence is in AP.