Grade 5

Read the Headline Story to students and write the sequence on the board. Encourage thinking about what the rule is (how big a jump from one number to the next), how many jumps would be needed to solve the problem, and how to solve the problem without writing all the in-between terms of the sequence.

A sequence of numbers starts 1, 99, 197, 295, 393, 491, 589, … and continues the same way forever. How could you find the 100^{th} number in this sequence?

- After the first, we keep increasing by 100 and decreasing by 2. Each is 98 more than the last. We need 99 jumps from 1 to get to the hundredth number. Ninety-nine jumps of 98 is 99 × 98. I can do that in my head 100 × 98 = 9,800, so 99 × 98 is 9,800 – 98, or 9,702. We jumped 9,702 from 1, so the hundredth number is 9,703.

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