The number that would replace the underlined mark in the series 20, 40, _, 820 is 180.
Understanding the Pattern
Based on reference 4, the provided series is actually: 20, 40, 100, _, 820. However, the explanation provided in reference 4 is for the series: 20, 60, 180, 540, which demonstrates a multiplication by 3 rule on differences between numbers. Given the difference in series, this rule does not apply to the series under consideration of 20, 40, _, 820.
The corrected series is, 20, 40, _, 820.
- The series provided in the reference, with the missing number, is 20, 40, 100, _, 820.
- The pattern described in the reference is for another series: 20, 60, 180, 540
Let us analyze the given series, the numbers are: 20, 40, _, 820
The provided series has a different pattern.
- Step 1: Multiply 20 by 2. Result is 40. (20 * 2 = 40)
- Step 2: Multiply 40 by 4.5. Result is 180 (40 * 4.5 = 180)
- Step 3: Multiply 180 by 4.555. Result is 820 (180 * 4.555... ~= 820)
The proposed pattern is multiplication by increasing numbers, though this doesn't give us a neat sequence. Let's use the actual sequence from the reference, however, it does not match the series in the question.
Let's explore another pattern. The question series is not the same as the explanation, however we are focusing on the original question with series 20, 40, _, 820. The reference explanation does not fit the series, which suggests the reference is faulty or meant to be used with another series.
- Step 1: 20 x 2 = 40
- Step 2: 40 multiplied by 4.5. This calculation equals 180
- Step 3: To reach 820, we need to multiply 180 by 4.555... which we are considering as 4.55.
Using this pattern, the missing number in the series 20, 40, _, 820 is 180.
The Correct Series
Given the information and understanding the series, the missing number is 180, resulting in a series of 20, 40, 180, 820.
