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xholicwriter
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Given N= 1.2.3 + 2.3.4 + ... + n(n+1)(n+2), prove that 4N + 1 is a square (n is a positive integer)
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. For example, in the sequence 3, 6, 9, 12, the difference between each term is 3.
The common difference in an arithmetic sequence can be found by subtracting any term from the term before it. This will give you the difference between consecutive terms, which is the same for the entire sequence.
Yes, an arithmetic sequence can have negative terms. As long as the difference between consecutive terms remains constant, the sequence is still considered arithmetic.
The formula for finding the nth term in an arithmetic sequence is:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, and d is the common difference.
Arithmetic sequences can be used in many real-life situations, such as calculating interest on a loan, tracking population growth, or predicting future values in financial investments. They can also be used in mathematical modeling to study patterns and make predictions in various fields, such as physics, economics, and biology.