1, 4, 9, 16, 25,... What is the next number in this sequence?
Understand the Problem
The question is asking to identify the pattern or sequence in the numbers provided. The sequence given includes perfect squares: 1 (1^2), 4 (2^2), 9 (3^2), 16 (4^2), and 25 (5^2). The task is to determine the next number in the sequence.
Answer
The next number in the sequence is $36$.
Answer for screen readers
The next number in the sequence is 36.
Steps to Solve
- Identify the pattern in the sequence
The given numbers are: 1, 4, 9, 16, 25. These correspond to the squares of consecutive integers:
- $1 = 1^2$
- $4 = 2^2$
- $9 = 3^2$
- $16 = 4^2$
- $25 = 5^2$
- Determine the next integer
The pattern shows that each number is the square of integers starting from 1 and increasing by 1 for each subsequent number. The next integer after 5 is 6.
- Calculate the next perfect square
To find the next number in the sequence, we calculate $6^2$: $$ 6^2 = 36 $$
The next number in the sequence is 36.
More Information
The sequence consists of perfect squares, which are numbers that can be expressed as the square of an integer. The perfect squares follow a well-known pattern that continues indefinitely.
Tips
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