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QUESTION

What is a possible explicit rule for the nth term of the sequence: 25, 15, 5, -5, -15?

a_n = 25-10(n-1)

An is a sequence in which there is a constant difference between successive terms. Given an arithmetic sequence with initial term a_1 and a constant difference d we can write the n^"th" term as a_n = a_1+d(n-1)

In this case, as each term is 10 less than the previous term, the sequence is potentially an arithmetic sequence with initial term 25 and constant difference -10, meaning we would have a_n = 25 -10(n-1)