Sum of odd integers

Algebra Level 2

Find the sum of all odd integers from 16 to 659 inclusive.


The answer is 108836.

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1 solution

If you aren't familiar with AP, refer the last of the solution.

Number of terms in an AP = l a d + 1 =\dfrac{l-a}{d}+1

In this case, n = 659 17 2 + 1 = 322 n=\dfrac{659-17}{2}+1=322

Sum of terms of AP = n 2 ( a + l ) =\dfrac{n}{2}(a+l) Here, sum = 322 2 ( 17 + 659 ) = 108836 =\dfrac{322}{2}(17+659)=108836


Note:

First term of an AP = a =a

Last term of an AP = l =l

Difference between 2 consecutive terms = d =d

Number of terms in an AP = n =n

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