Step 1
We know the arithmetic sequence is a sequence whose difference between two consecutive terms is constant. The geometric sequence is a sequence whose ratio of two consecutive terms is constant.
The nth term of the sequence is
\(a_n = 5 + \sqrt{2n}\)

\(a_{n+1} = 5 + \sqrt(2{n+1})\) Step 2 Difference between two consecutive terms is \(a_{n+1} - a_n = [5 + \sqrt{2(n+1)}] - (5 + sqrt\{2n})\)

\(a_{n+1} - a_n = \sqrt2\) which is constant Therefore, nth term defines an arithmetic sequence Common difference is \(d = \sqrt2\) Step 3 Amns: nth term defines an arithmetic sequence Common difference is \(d = \sqrt2\)

\(a_{n+1} = 5 + \sqrt(2{n+1})\) Step 2 Difference between two consecutive terms is \(a_{n+1} - a_n = [5 + \sqrt{2(n+1)}] - (5 + sqrt\{2n})\)

\(a_{n+1} - a_n = \sqrt2\) which is constant Therefore, nth term defines an arithmetic sequence Common difference is \(d = \sqrt2\) Step 3 Amns: nth term defines an arithmetic sequence Common difference is \(d = \sqrt2\)