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Write a recursive formula for an, the nth term of the sequence 1, -2, -5,…

We need two things to write the recursive formula

is the first value of this sequence. For this set of values, , since appears first.

, the common difference, is . Basically it's just the the higher term minus the previous terms. To solve for ,

So regardless of what terms you choose, the common difference will be the same. Now the general formula for a recursive function is

where is the term. Let's substitute for and in this formula.

So the recursive formula is

yes. we do proportions in probabilities.