I am having trouble finding the next two numbers in this series:
1, 1/4, 1/9, 1/16, ...
HINT:
numerator is always 1
denominator is always...
1/1
1/(1+3) = 1/4
1/(4+5) = 1/9
1/(9+7) = 1/16
...
To find the next numbers in this series, we need to identify the pattern. In this case, the series appears to be decreasing squares of numbers. Let's break it down step by step:
1. The first number in the series is 1, which can be written as 1/1^2.
2. The next number is obtained by taking the square of the next natural number (2) and then taking its reciprocal: 1/(2^2) = 1/4.
3. The third number is obtained by taking the square of the next natural number (3) and then taking its reciprocal: 1/(3^2) = 1/9.
4. By following this pattern, the fourth number is obtained by taking the square of the next natural number (4) and then taking its reciprocal: 1/(4^2) = 1/16.
To find the next two numbers, we continue the pattern:
- The fifth number is the reciprocal of the square of the next natural number (5): 1/(5^2) = 1/25.
- The sixth number would be the reciprocal of the square of the next natural number (6): 1/(6^2) = 1/36.
Therefore, the next two numbers in the series are 1/25 and 1/36.