What is the 200th Number?

What is the 200th 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 200th term.

The first term of the sequence is 2.

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

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

2 + 5 (199) = 997

The 200th term is 997.

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