Question 4 the day: April 21, 2003
The question for the day is from the topic AP and GP. The question is about finding the sum of a series of numbers that are in Arithmetic Progression

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

(1) 10050
(2) 5050
(3) 5000
(4) 50000

Correct Answer is 50,000 and Correct Choice is (4)

Explanatory Answer

The positive integers, which are divisible by 5, are 5, 10, 15, ..., 1000
Out of these 10,20,30,.... 1000 are divisible by 2
Thus, we have to find the sum of the positive integers 5, 15, 25, ...., 995

If n is the number of terms in it the sequence then
995 = 5 + 10(n - 1) => 1000 = 10n
Therefore, n = 100.
Thus the sum of the series = (n/2)(a + l) = (100/2) (5 + 995) = 50000.

Question on finding sum of terms of a GP, Problem on finding a particular term of an AP, given sum of two other terms, Summation of AP having negative common difference, Finding terms of an AP, given sum and product of some of its terms, Sum of series of numbers in arithmetic progression, A CAT 2003 question to find sum of terms of an AP

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