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. an=5±2n
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Obiajulu
Answered 2020-12-25 Author has 98 answers

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 an=5+2n
an+1=5+(2n+1) Step 2 Difference between two consecutive terms is an+1an=[5+2(n+1)](5+2n)
an+1an=2 which is constant Therefore, nth term defines an arithmetic sequence Common difference is d=2 Step 3 Amns: nth term defines an arithmetic sequence Common difference is d=2

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