 # For Exercise, determine if the nth term of the sequence defines an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference d. If the sequence is geometric, find the common ratio r. a_{n} = 5 pm sqrt{2n} tabita57i 2020-12-24 Answered
For Exercise, determine if the nth term of the sequence defines an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference d. If the sequence is geometric, find the common ratio r. ${a}_{n}=5±\sqrt{2n}$
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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 ${a}_{n}=5+\sqrt{2n}$
${a}_{n+1}=5+\sqrt{\left(}2n+1\right)$ Step 2 Difference between two consecutive terms is ${a}_{n+1}-{a}_{n}=\left[5+\sqrt{2\left(n+1\right)}\right]-\left(5+\sqrt{2n}\right)$
${a}_{n+1}-{a}_{n}=\sqrt{2}$ which is constant Therefore, nth term defines an arithmetic sequence Common difference is $d=\sqrt{2}$ Step 3 Amns: nth term defines an arithmetic sequence Common difference is $d=\sqrt{2}$