Sum of numbers from 250 to 1000 which are divisible by 3 is

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8. Sequences and Series

easy

The sum of numbers from $250$ to $1000$ which are divisible by $3$ is

A

$135657$

B

$136557$

C

$161575$

D

$156375$

Solution

(d) The number divisible by $3$ between $250$ to $1000$ are $252, 255, ….., 999.$

$\therefore $${T_n} = 999 = 252 + (n – 1)3$

$ \Rightarrow $$333 = 84 + n – 1$

$ \Rightarrow $ $n = 250$

$\therefore $ $S = \frac{n}{2}[a + l] = \frac{{250}}{2}[252 + 999]$

= $125 \times 1251 = 156375$.

Standard 11

Mathematics

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