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

Concept / Approach

• This is an arithmetic series with first term 51, last term 100, and common difference 1.
• Use the sum formula Sn = n(First + Last) / 2 where n = 100 − 51 + 1 = 50.

Step-by-step calculationn = 50S = 50 × (51 + 100) / 2= 50 × 151 / 2= 25 × 151 = 3775

VerificationPairing terms: (51 + 100), (52 + 99), … each pair sums to 151; there are 25 pairs ⇒ 25 × 151 = 3775.

Common pitfalls

• Using 50 × 151 (forgetting to divide by 2) or taking the wrong number of terms.

Final Answer3775