2, 212, 422, 3, 313, 623, ...
What are the next 3 numbers?
When I say that this my favorite math problem, I mean problems similar to this where the next few terms must be found. I like the idea of creating sequences and series to solve a rather confusing question. When problem solving, one must look for a pattern in order to set up an alternating series or a summation. In this case, I made a problem where your initial value is n(0) = 2. The next two terms, n(1) and n(2) are created by adding 210 respectively. The fourth term, n(3), seems to be n(0) + 1 where the following two terms are created by adding 310 respectively. After finding this pattern, one must create a sequence in order to predict n(6), n(7) and n(8).
Hint: n(1) = n(0) + 210 and n(2) = n(1) + 210.
Hint: n(3) = n(0) + 1.
Hint: n(3) = n(0) + 1.
Solution: Since the next term, n(6), follows two terms that 310 were added, we know it must be of the from n(3) + 1 in order to follow the pattern. Thus, n(6) = 4. The next term, n(7), must be of the form n(6) + 100[n(6)] + 10, which is 4 + 400 + 10 = 414. Since n(7) = 414 and n(8) must be of the form n(7) + 410, then n(8) = 824.