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Number sequences may contain exponential numbers, with terms generally raised to the power of two or three.
Example 1
{1, 16, 81, 256, ?}
Answer: 5^4 = 625
Explanation: Integers, in increasing order, to the power of four.
1^4=1, 2^4=16, 3^4=81, 4^4=256, 5^4=625
Example 2
{46656, 3125, 256, 27, 4, 1, ?}
Answer: 0^1 = 0
Explanation: Starting from six, raise each number to the power of itself.
6^6=46656, 5^5=3125, 4^4=256, 3^3=27, 2^2=4, 1^1=1, 0^1=0
1. {36, 80, 150, 252, ?}
Answer: 392
Progression: {3^2 +3^3, 4^2 +4^3, 5^2+5^3, 6^2 + 6^3, 7^2 + 7^3 = 392}
2. {2, 8, 18, 32, 50, ?}
Answer: 2x(6^2) = 72
Explanation: 2x1^2, 2x2^2, 2x3^2, 2x4^2, 2x5^2
3. {8, 1, 64, 9, 216, 25, ?}
Answer: 8^3 = 512
Explanation: Even items are cubes of 2,4,6, while the odd items are squares of 1,3,5
4. {3, 8, 15, 24, 35}
Answer: (6^2) - 1 = 48
Explanation: (2^2 - 1), (3^2 - 1), (4^2 - 1), (5^2 - 1)
5. {4, 16, 36, 64, ?, 144, 196}
Answer: (14^2) = 196
Explanation: Squares of even numbers.