NIMCET 2023 — Reasoning PYQ

Step-by-step Solution 

 

1. The differences between consecutive terms in the given series are calculated: 

• The difference between the second term and the first term is $10-3=7$. 

• The difference between the third term and the second term is $24-10=14$. 

• The difference between the fourth term and the third term is $45-24=21$. 

• The difference between the fifth term and the fourth term is $73-45=28$. 

2. A pattern is observed in these differences: $7,14,21,28$. It is noted that each subsequent difference is greater than the previous one by $7$. This indicates an arithmetic progression of differences with a common difference of $7$. 

3. To find the next term in the series, the next difference in the pattern is determined. Following the established pattern, the next difference after $28$ should be $28+7=35$. 

4. This calculated difference is added to the last known term in the series to find the missing term: $73+35=108$. [1]  

Final Answer 

The next number in the series is $108$.