Evaluate the sum: 51 + 52 + 53 + … + 100.

Given data

• Consecutive integers from 51 to 100 inclusive.

Concept / Approach

• Arithmetic series: S = n/2 × (first + last) or S = n × average.

Step-by-step calculation

Number of terms n = 100 − 51 + 1 = 50Average = (51 + 100)/2 = 151/2 = 75.5Sum S = n × average = 50 × 75.5 = 3,775

Verification / Alternative

Pairing method: (51+100), (52+99), … each pair = 151; 25 pairs ⇒ 25 × 151 = 3,775.

Common pitfalls

• Forgetting to include both endpoints 51 and 100.

Final Answer

3775