What is the 200^{th} number in the arithmetic sequence: 2, 7, 12, 17, 22, 27, 32, …?

**Answer**

We need to answer two questions to get to the answer. First, we have to find what is the common difference in this sequence (ie the difference between any two consecutive terms).

Second, we need to determine how many times do we have to add the common difference to the first term in order to arrive at the 200^{th} term.

The first term of the sequence is 2.

The common difference is 7 – 2 = 12 – 7 = 22 – 17 = … = 5

To get to the 200^{th} term, we must add the common difference 199 times:

2 + 5 (199) = 997

The 200^{th} term is 997.

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