Sum of integers from 1 to 100 that are divisible by 2 or 5 is

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8. Sequences and Series

medium

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

$3000$

$3050$

$4050$

None of these

(IIT-1984)

Solution

(b) The sum of integers from $1$ to $100$ that are divisible by $2$ or $5 =$ sum of series divisible by $2 +$ sum of series divisible by $5 -$ sum of series divisible by $2$ and $5$.

$ = (2 + 4 + 6 + …… + 100) + (5 + 10 + 15……. + 100)$

$ – (10 + 20 + 30 + …….. + 100)$

$ = \frac{{50}}{2}\left\{ {2 \times 2 + (50 – 1)2} \right\} + \frac{{20}}{2}\left\{ {2 \times 5 + (20 – 1)5} \right\}$

$ – \frac{{10}}{2}\left\{ {10 \times 2 + (10 – 1)10} \right\}$

$ = 2550 + 1050 – 550 = 3050$.

Standard 11

Mathematics

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medium

(JEE MAIN-2022)

Suppose we have an arithmetic progression $a_1, a_2, \ldots a_n, \ldots$ with $a_1=1, a_2-a_1=5$. The median of the finite sequence $a_1, a_2, \ldots, a_k$, where $a_k \leq 2021$ and $a_{k+1} > 2021$ is

hard

(KVPY-2021)

If $x,y,z$ are in $A.P. $ and ${\tan ^{ – 1}}x,{\tan ^{ – 1}}y$ and ${\tan ^{ – 1}}z$ are also in $A.P.$, then

medium

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hard

(JEE MAIN-2025)

If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be

easy

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

Solution

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