Find the missing term in the following series. $0,4,18,48 , ? , 180$
- $100$
- $191$
- $152$
- $110$
Reveal answer
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A
Correct answer
Explanation
Differences: 4-0=4, 18-4=14, 48-18=30. Second differences: 14-4=10, 30-14=16. Third difference is 6. Next second difference = 16+6=22. Next first difference = 30+22=52. Next term = 48+52=100.
AI explanation
The given series is based on the sum of cubes of natural numbers, but we will look at the pattern of multiplying the position number by a perfect square: $0 = 0 \times 1^2$, $4 = 1 \times 2^2$, $18 = 2 \times 3^2$, and $48 = 3 \times 4^2$. Following this pattern, the fifth term is $4 \times 5^2 = 100$. This logic perfectly continues as the sixth term is $5 \times 6^2 = 180$, making the missing term 100.