Write the next elements in the series.2 4 16 512 _

Solution: Find the next term in the series.

• Express each term as a power of 2: 2 = 2^1, 4 = 2^2, 16 = 2^4, 512 = 2^9.

• The exponents are 1, 2, 4, 9. The differences between consecutive exponents are 1, 2, 5.

• The second differences are 1 and 3. These increase by 2, so the next second difference is 5. Add this to the last first-difference (5) to get the next first-difference 10.

• Therefore the next exponent = 9 + 10 = 19, and the next term = 2^19 = 524,288.

Answer: 524288