Question

Find the missing term in the series: \[ 50,\;40,\;33\frac{1}{3},\;28\frac{4}{7},\;\_\_\_,\;22\frac{2}{9},\;20,\;18\frac{2}{11},\;16\frac{2}{3} \]

• A. \(25\)
• B. \(24\frac{2}{7}\)
• C. \(23\frac{1}{9}\)
• D. \(23\frac{5}{9}\)

Hint:

For fractional series, first convert mixed fractions properly and then check the difference pattern.

Answer 1

The Correct Option is A

Concept: Observe the pattern of subtraction. The numbers are decreasing by fractions: \[ -10,\;-\frac{20}{3},\;-\frac{10}{21},\;-\frac{25}{7},\dots \] A better way is to convert into improper fractions and compare.

Step 1: Write all terms clearly.
\[ 50 \] \[ 40 = 50-10 \] \[ 33\frac{1}{3}=40-\frac{20}{3} \] \[ 28\frac{4}{7}=33\frac{1}{3}-\frac{10}{21} \] Looking carefully, the series approximately decreases by: \[ 10,\;\frac{20}{3},\;\frac{10}{7},\;\frac{25}{7},\;\frac{25}{9},\;\frac{20}{9},\;\frac{20}{11},\;\frac{40}{33} \]

Step 2: Identify the main pattern.
The simpler structure is: \[ 50,\;40,\;33\frac13,\;28\frac47,\;25,\;22\frac29,\;20,\;18\frac2{11},\;16\frac23 \] This follows subtraction: \[ 10,\;\frac{20}{3},\;\frac{10}{7},\;\frac{25}{7},\;\frac{25}{9},\;\frac{20}{9},\;\frac{20}{11},\;\frac{16}{11} \] Thus the missing number fitting the decreasing trend is: \[ 25 \] Hence, the required term is: \[ \boxed{25} \]