Find the sum of all two-digit numbers that are divisible by 5

Concept / Approach

• Two-digit multiples of 5 are 10, 15, …, 95 (arithmetic sequence with d = 5).
• Use the sum formula for an arithmetic series.

Step-by-step calculationFirst = 10, Last = 95, d = 5Number of terms n = ((95 − 10)/5) + 1 = 18Sum S = n(First + Last)/2 = 18 × (10 + 95)/2= 18 × 105 / 2 = 9 × 105 = 945

VerificationPair terms (10 + 95), (15 + 90), … each = 105; 9 pairs ⇒ 9 × 105 = 945.

Final Answer945