Question

Find the common difference of the following arithmetic progression.
$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$

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

Answer 1

The correct option is A

$2\sqrt{2}$

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

Hence, we can conclude that the common difference of the given AP is $2\sqrt{2}.$