Question

The common difference for the arithmetic progression
$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$ is

• A. $3+\sqrt{2}$
• B. $3$
• C. $2\sqrt{2}$

Answer 1

The correct option is C $2\sqrt{2}$

Given A.P is
$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$
Common difference is the difference between two consecutive terms in an arithmetic sequence.
$(3+4\sqrt{2})-(3+2\sqrt{2})=2\sqrt{2}$
$(3+6\sqrt{2})-(3+4\sqrt{2})=2\sqrt{2}$
$(3+8\sqrt{2})-(3+6\sqrt{2})=2\sqrt{2}$