Question

Numbers between 400 to 500 that divisible by 3

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

The Numbers between 400 to 500 that divisible by 3

EVALUATION

The first and the last number between 400 to 500 that divisible by 3 is 402 and 498

So the progression is

402 , 405 , 408 , ................ , 498

This is an Arithmetic progression with

First term = a = 402

Common Difference = d = 3

Let there are n numbers between 400 to 500 that divisible by 3

So nth term = 498

$\implies \sf{ a + (n - 1)d =498\: }$

$\implies \sf{ 402+ 3(n - 1) =498\: }$

$\implies \sf{ 3(n - 1) = 96\: }$

$\implies \sf{ (n - 1) =32\: }$

$\implies \sf{ n = 33\: }$

Hence there are 33 numbers between 400 to 500 that divisible by 3

The numbers are

402 , 405 , 408 , 411 , 414, 417, 420, 423,426, 429, 432, 435, 438, 441, 444, 447, 450,453,

456,459,462,465,468,471,474,477,

480,483,486, 489,492,495 , 498

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