What is the next number: 1, 4, 27, 16, 125, 36, __?

We have to find the pattern sequence followed by the numbers in the sequence 1, 4, 27, 16, 125, 36 to find the next number.

Answer: The next number in the given series is 343.

Let us understand the problem with an explanation.

Explanation:

From the given series, we see that:

• 1 is the square and cube of 1
• 4 is the square of 2
• 27 is the cube of 3
• 16 is the square of 4
• 125 is the cube of 5
• 36 is the square of 6

Hence, the pattern is cubes and squares of alternate numbers in the series, that is, 1³, 2², 3³, 4², 5³, 6².......

Therefore, the next number is 7³ = 343.

Hence, the next number in the given series is 343.