Sequences And Series Ques 46
The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is …..
$(1984,2 M)$
Show Answer
Answer:
Correct Answer: 46.$(3050)$
Solution:
Formula:
An Arithmetic Progression (A.P.):
- 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} $
BETA
