Question : What is the sum of all two-digit odd numbers?
Option 1: 2375
Option 2: 2475
Option 3: 2325
Option 4: 2425
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Correct Answer: 2475
Solution :
Use the formulas:
n
th
term = first term + (n – 1) × common difference
Sum of an arithmetic sequence, S = $\frac{\text{number of terms}}{2}×\text{(first term + last term)}$
Two-digit odd numbers : 11,13,15, ........, 97, 99
Common difference = 2
Number of terms, n $=\frac{(99-11)}{2} + 1 = 44 + 1 = 45$
Sum of an arithmetic sequence, S $=\frac{45}{2}×(11+99) = 22.5 × 110 = 2475$
Hence, the correct answer is 2475.
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