Explanation:

Let's analyze the series: 1, 4, 9, 16, 27, ?

- The first four numbers are 1², 2², 3², 4²: 1, 4, 9, 16.

- The next number, 27, breaks the square pattern. 27 is 3³.

- Let's see if there's a new pattern:

- 1 (1²)

- 4 (2²)

- 9 (3²)

- 16 (4²)

- 27 (3³)

Let’s guess the next:

- After 4² = 16, then 3³ = 27, perhaps 4³ = 64?

- But none of the options are 64.

Let's look if there's any pattern based on differences:

- 4 – 1 = 3

- 9 – 4 = 5

- 16 – 9 = 7

- 27 – 16 = 11

The differences are: 3, 5, 7, 11 (all are odd numbers, and mostly primes)

- Next difference, possibly 13 (the next odd prime)

- 27 + 13 = 40

So, the next number is 40.

Reviewing options

- Option 1: 35 (No, 27 + 8 = 35, doesn’t fit pattern)

- Option 2: 43 (27 + 16 = 43, 16 is not part of differences sequence)

- Option 3: 32 (27 + 5 = 32, doesn’t fit pattern)

- Option 4: 40 (27 + 13 = 40, fits the next odd prime difference )

- Option 5: 50 (27 + 23 = 50, doesn’t fit the sequence)

Correct answer: Option 4 - 40