Sequences and Series 2 Question 16
17. The sum of integers from 1 to 100 that are divisible by 2 or 5 is …..
$(1984,2 M)$
Analytical & Descriptive Questions
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Answer:
Correct Answer: 17. (5)
Solution:
- Integers divisible by 2 are ${2,4,6,8,10, \ldots, 100}$.
Integers divisible by 5 are ${5,10,15, \ldots, 100}$.
Thus, sum of integers divisible by 2
$$ =\frac{50}{2}(2+100)=50 \times 51=2550 $$
Sum of integers divisible by 5
$$ =\frac{20}{2}(5+100)=10 \times 105=1050 $$
Sum of integers divisible by 10
$$ =\frac{10}{2}(10+100)=5 \times 110=550 $$
$\therefore$ Sum of integers from 1 to 100 divisible by 2 or 5
$$ \begin{aligned} & =2550+1050-550 \\ & =2550+500=3050 \end{aligned} $$
