Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.)5, 7, 9, 11, 13, . . .
Question
Write an expression for the apparent nth term of the sequence.
(Assume that n begins with 1.)
5, 7, 9, 11, 13, . . .
Solution
The given sequence is an arithmetic sequence, where each term increases by a common difference. In this case, the common difference is 2 (7-5 = 2, 9-7 = 2, etc.).
The nth term of an arithmetic sequence can be found using the formula:
a_n = a_1 + (n-1)*d
where:
- a_n is the nth term
- a_1 is the first term
- d is the common difference
- n is the term number
For this sequence:
- a_1 = 5 (the first term)
- d = 2 (the common difference)
So, the nth term of the sequence is given by:
a_n = 5 + (n-1)*2
Simplifying this expression gives:
a_n = 3 + 2n
So, the apparent nth term of the sequence 5, 7, 9, 11, 13, . . . is 3 + 2n.
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