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

Solution:

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.

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.

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

Summary:

The next number in the given series is 343.