SATHEE: Sequences and Series 2 Question 16

Sequences and Series 2 Question 16

17.

The sum of integers from 1 to 100 that are divisible by 2 or 5 is …..

$(1984, 2 M)$

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Answer:

Correct Answer: 17. $(3050)$

Solution:

Integers divisible by 2 are $(2, 4, 6, 8, 10, \dots, 100)$ .

Integers divisible by 5 are $(5, 10, 15, \dots, 100)$ .

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

$= \frac{10}{2} (10 + 100) = 5 \times 110 = 550$

$∴$ Sum of integers from 1 to 100 divisible by 2 or 5

$\begin{aligned} = 2550 + 1050 - 550 \\ = 2550 + 500 = 3050 \end{aligned}$

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Sequences and Series 2 Question 16

17.

Answer:

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