What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?
A. 10,050
B. 5050
C. 5000
D. 50,000
Answer: Option D
Solution(By Examveda Team)
The positive integers, which are divisible by 5 are 5, 10, 15, ....., 1000Out 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
∴ n = 100
Thus the sum of the series
$$\eqalign{ & = \left( {\frac{n}{2}} \right)\left( {a + l} \right) \cr & = \left( {\frac{{100}}{2}} \right)\left( {5 + 995} \right) \cr & = \frac{{100 \times 1000}}{2} \cr & = 50000 \cr} $$
Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
Join The Discussion