$\frac{2}{3}, 2, 4, \frac{20}{3}, ?$
Series Pattern Analysis
The given number series is:
\(\frac{2}{3}, 2, 4, \frac{20}{3}, ?\)
Series Terms Common Denominator
To identify the pattern, it is helpful to express all terms with a common denominator. The least common denominator here is 3:
- Term 1: \(\frac{2}{3}\)
- Term 2: \(2 = \frac{2 \times 3}{3} = \frac{6}{3}\)
- Term 3: \(4 = \frac{4 \times 3}{3} = \frac{12}{3}\)
- Term 4: \(\frac{20}{3}\)
The series, when expressed with a denominator of 3, becomes: \(\frac{2}{3}, \frac{6}{3}, \frac{12}{3}, \frac{20}{3}, ?\)
Series Numerator Pattern
Now, let's examine the sequence formed by the numerators:
2, 6, 12, 20, ?
Calculate the differences between consecutive numerators:
- \(6 - 2 = 4\)
- \(12 - 6 = 6\)
- \(20 - 12 = 8\)
The sequence of differences is 4, 6, 8. This is an arithmetic progression where each term increases by 2.
Series Next Term Calculation
Following the pattern of differences (4, 6, 8), the next difference should be \(8 + 2 = 10\).
To find the next numerator, add this difference (10) to the last numerator (20):
\(N_5 = 20 + 10 = 30\)
The fifth term of the series will have this numerator (30) and the common denominator (3):
Term 5 = \(\frac{30}{3} = 10\)
Conclusion
The number that replaces the question mark is 10.
Similar Questions
- What should come in place of the question mark (?) in the given series?
160 151 140 127 112 ? - What should come in place of the question mark (?) in the given series?
3, −2, −12, −32, −72, ? - What should come in place of the question mark (?) in the given series?
512 513 505 532 468 ? - What should come in place of the question mark (?) in the given series?
98 102 110 126 158 ? - What should come in place of the question mark (?) in the given series?
679 680 690 691 701 702 712 ? - What should come in place of the question mark (?) in the given series?
7 13 25 43 67 ? Select the number from among the given options that will come next in the following series.
$0, 6, 25, 62$, _________
- Select the number from among the given options that can replace the question mark (?) in the following series.
13, 25, 49, 97, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
1, 1, 3, 5, 11, 21, 43, ? - Select the number that can replace the question mark (?) in the following series.
1, 5, 32, 288 ?
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
