Complete the pattern: 120, 96, 76.8, 61.44, ?

Question

Complete the pattern: 120, 96, 76.8, 61.44, ?

1. A. 60.27
2. B. 78.91
3. C. 47.89
4. D. 49.152 (Correct answer)

Correct Answer

Option D — 49.152

Detailed Solution & Explanation

The correct answer is 49.152.

Key Points

• Check the ratio between consecutive terms rather than the difference:
  • 96 ÷ 120 = 0.8, 76.8 ÷ 96 = 0.8, 61.44 ÷ 76.8 = 0.8
• The series is geometric with a common ratio of 0.8 (that is, each term is 4/5 of the previous one).
• Next term = 61.44 × 0.8 = 49.152.

Additional Information

• When terms decrease and the differences are not constant, test the ratio first — a decimal series shrinking steadily is almost always geometric.
• Using the fraction 4/5 rather than 0.8 keeps the arithmetic exact: 61.44 × 4 = 245.76, divided by 5 = 49.152.
• The nth term of a geometric progression is arⁿ⁻¹, and the number of decimal places grows by one at each step here — a quick visual check that immediately rules out the two-decimal options.

प्रश्न (हिन्दी में)

श्रृंखला को पूरा करें: 120, 96, 76.8, 61.44, ?

1. A. 60.27
2. B. 78.91
3. C. 47.89
4. D. 49.152