Question

Complete the series 564, 152, 48, 21,_? from the following options :

• A. 132
• B. 24.2
• C. 15.25
• D. 13.25

Answer 1

The Correct Option is D

To solve the problem of completing the series 564, 152, 48, 21, _?, we need to analyze the pattern between the numbers given in the series: 

1. First, consider the differences between consecutive terms of the series:
   • The difference between 564 and 152 is \( 564 - 152 = 412 \).
   • The difference between 152 and 48 is \( 152 - 48 = 104 \).
   • The difference between 48 and 21 is \( 48 - 21 = 27 \).
2. Next, evaluate the pattern of the differences between the terms:
   • Notice that 412, 104, and 27 form their own decreasing sequence. Let's check the pattern in this sequence:
     • The difference between 412 and 104 is \( 412 - 104 = 308 \).
     • The difference between 104 and 27 is \( 104 - 27 = 77 \).
   • Observing the differences (308 and 77) further down, they do not follow a straightforward arithmetic progression. Thus, let's explore another approach such as division or fractions.
3. Observe if division of terms might result in a consistent pattern:
   • \( \frac{564}{152} \approx 3.71 \)
   • \( \frac{152}{48} \approx 3.17 \)
   • \( \frac{48}{21} \approx 2.29 \)
4. Now, let's try calculating each term by dividing with decreasing factors:
5. If we divide the initial term by approximately 3.7, we get close to the next term, so continue this apparent pattern decreasing each factor:
   • \( 21 \div (\approx 1.59) \approx 13.25 \)
6. This division approach reveals an approximate sequence where decreasing factors yield the next term.

Therefore, the missing term is approximately calculated as 13.25, making

13.25

the correct answer for completing the series.

 

Thus, the correct option is: 13.25.