Find the Sum

Number Theory Level 3

Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

Hint: The numbers are not divisible by 2 but divisible by 5. So, the numbers are all odd numbers.


The answer is 50000.

Samara Simha Reddy by Samara Simha Reddy , 22, India

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3 solutions

Consider numbers 5 , 15 , 25 , 35 , . . . . . . . . . . , 995 5,15,25,35,..........,995 Last term, l = a + ( n − 1 ) × d l = a + (n-1) \times d

a = 5 ; d = 10 ; l = 995 a = 5; d = 10; l = 995

Therefore, n = 100. n = 100.

Using Sum formula

S = n 2 × ( a + l ) S = 100 2 × ( 5 + 995 ) S = 50 × 1000 ∴ S = 50000 . \large \displaystyle S = \frac{n}{2} \times (a + l)\\ \large \displaystyle S = \frac{100}{2} \times (5+995)\\ \large \displaystyle S = 50 \times 1000\\ \large \displaystyle \therefore S = \color{#3D99F6}{\boxed{50000}}.

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Ramiel To-ong
Feb 2, 2016

nice solution

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Ashwin K
Feb 2, 2016

Another approach to this :

Series is 5, 15, 25,.....,995 

Middle term = (5+995)/2 = 500
No. of terms(n) = (995 - 5)/10+1 = 100
Sum of the series = (middle term) (n) = 50000//
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