What is the next number in the sequence 7 10 16 28...?

Answer 1

What number would you like to be next?

u(1) = 7

u(2) = 10 = u(1) + 3

u(3) = 16 = u(2) + 6

u(4) = 28 = u(3) + 12

The amount added on each time doubles

→ u(5) = u(4) + 2 × 12 = 28 + 24 = 52

Alternatively:

u(n) = (x³ - 3x² + 8x - 8)/2

→ u(1..4) = {7, 10, 16, 28}

→ u(5) = 5³ - 3 × 5³ + 8 × 5 - 8)/2 = 49

Or:

u(n) = (-7x⁴ + 82x³ - 281x² + 446x - 72)/24

→ u(1..4) = {7, 10, 16, 28}

→ u(5) = (-7 × 5⁴ + 82 × 5³ - 281 × 5² + 446 × 5 - 72)/24 = 42