Estimating next term
Second difference
Ex) 1, 4, 10, 20, 35, 56, 84, ?
First differences: 3, 6, 10, 15, 21, 28 Second differences: 3, 4, 5, 6, 7
So ans = 84+28+8 = 120
Fraccions
Ex) 1.333, 1.25, 1.2, 0.875, 0.8889, ? In fraction: 4/3, 5/4, 6/5, 7/8, 8/9, ? Ans: 9/10
Combinations of sequences
Ex) 18, 225, 22, 13, 45, 16, 8, 9, 10, ?
- Seq #1: 18, 13, 8 is a sequence decreasing by 5
- Seq #2: 225, 25, 9 is a sequence decreasing by a factor of 1/5
- Seq #3: 22, 16, 10 is decreasing by 6.
Planets
Ex) MVEM → J
Mercury, Venus, earth, mars, jupiter, Saturn, Uranus, Neptune.
Recursive function differences
9,15, 24, 39, 63, 102,
We note that they are all divisible by 3:
3, 5, 8, 13, 21, 34
Now this is a simplerecursive function of degree 2.
Our number of interest is 21+34 = 55 And final answer: 55*3 = 165 (using 11)