Question
Download Solution PDFWhat is the sum of all two digit odd numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept Used:
The sum (S) of an arithmetic sequence can be calculated using the formula:
S = n/2 × (a + l)
where:
S is the sum of the sequence,
n is the number of terms,
a is the first term, and
l is the last term.
The number of terms (n) in an arithmetic sequence can be found using the formula:
n = (last term - first term)/difference + 1
Calculation:
Two-digit odd numbers range from 11 to 99. Since they are odd, they increase by a difference of 2 each time, forming an arithmetic sequence.
Number of terms (n):
n = (99 - 11)/2 + 1 = 44 + 1 = 45
Sum of an arithmetic sequence:
S = 45/2 × (11 + 99) = 22.5 × 110 = 2475
Therefore, the sum of all two-digit odd numbers is 2475.
∴ Option 2 is the correct answer.
Last updated on May 28, 2025
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