Question
Download Solution PDFWhat is the sum of all odd numbers up to 240?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
We need to find the sum of all odd numbers up to 240.
Concept Used:
The sum of the first n odd numbers is given by the formula S = n2, where n is the number of terms.
Calculation:
We need to determine the number of odd numbers up to 240.
⇒ The sequence of odd numbers up to 240 is: 1, 3, 5, ..., 239
⇒ This is an arithmetic sequence with the first term a = 1 and the common difference d = 2.
⇒ The nth term of an arithmetic sequence is given by the formula: an = a + (n - 1)d
⇒ Setting the nth term to 239, we get: 239 = 1 + (n - 1) × 2
⇒ 239 = 1 + 2n - 2
⇒ 239 = 2n - 1
⇒ 240 = 2n
⇒ n = 120
So, there are 120 odd numbers up to 240.
⇒ Using the formula for the sum of the first n odd numbers:
⇒ S = n2
⇒ S = 1202
⇒ S = 14400
∴ The sum of all odd numbers up to 240 is 14400.
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