The nth term of the sequence 7, 11, 15, 19, 23... is 4n + 3.
Understanding the Sequence
This is an arithmetic sequence, meaning there's a constant difference between consecutive terms. Let's break down why the formula 4n + 3 works:
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The Difference: Notice that each term is 4 more than the previous term (11 - 7 = 4, 15 - 11 = 4, etc.). This constant difference of 4 is key.
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Relating to 4n: A sequence with a common difference of 4 can be represented by 4n, where n is the term number (1, 2, 3, ...). However, the sequence 4n (which would be 4, 8, 12, 16, 20...) doesn't match our original sequence (7, 11, 15, 19, 23...).
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The Adjustment: As stated in the reference, to get the terms in our original sequence, we need to add 3 to each of the terms in the 4n sequence.
Deriving the Formula
Therefore, the nth term of the sequence is given by:
nth term = 4n + 3
Let's verify with a few examples:
- n = 1: 4(1) + 3 = 7 (Correct!)
- n = 2: 4(2) + 3 = 11 (Correct!)
- n = 3: 4(3) + 3 = 15 (Correct!)
The formula accurately generates the terms of the sequence.
