Question

Find the Sum of the Odd Integers between 80 and 262.

Answer 1

15561

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Identify the first (f) and last (l) odd numbers within this range and then use the sum of the arithmetic sequence formula.

The first odd number after 80 is 81 and the last odd number before 262 is 261.

We can calculate the total number of odd numbers (n) in this range using the formula:

• 
  `n = \cfrac{l -f}{2} +1`

Which gives us:

• 
  `n = \cfrac{261-81}{2} +1 =91\ total\ odd\ numbers`

Now, we can use the sum of an arithmetic series formula given by:

• 
  `S = (n/2) * (f + l)`

Thus, the sum is:

• 
  `S = (91/2) * (81 + 261) = 45.5 * 342 = 15561`