Question 4

1. Examine the terms of the series:

   $$2, 5, 10, 17, 26, 37, 50, 64$$

2. Observe the relation of each term to perfect squares $n^2 + 1$ for integers $n = 1, 2, 3, \dots$:

   • For $n = 1$: $1^2 + 1 = 2$
   • For $n = 2$: $2^2 + 1 = 5$
   • For $n = 3$: $3^2 + 1 = 10$
   • For $n = 4$: $4^2 + 1 = 17$
   • For $n = 5$: $5^2 + 1 = 26$
   • For $n = 6$: $3^2 + 1 = 37$
   • For $n = 7$: $7^2 + 1 = 50$
   • For $n = 8$: $8^2 + 1 = 65$

3. The given eighth term is $64$, whereas the pattern requires $65$ ($8^2 + 1$).

Therefore, the number that does not belong in the series is $64$ (option C).