Question

200 एवं 600 के बीच की उन समस्त संख्याओं का
योगफल क्या होगा, जो 16 से विभाज्य हो?​

Answer 1

SOLUTION

TO DETERMINE

The sum of all numbers between 200 and 600 which are divisible by 16

EVALUATION

Here the numbers between 200 and 600 which are divisible by 16 are

208 , 224 , 240 ,...., 592

This is an arithmetic progression

First term = a = 208

Common Difference = d = 16

Let 592 be the n th term of the AP

∴ a + ( n-1)d = 592

$\implies \sf{208 + 16(n - 1) = 592}$

$\implies \sf{ 16(n - 1) = 384}$

$\implies \sf{ (n - 1) = 24}$

$\implies \sf{ n = 25}$

So there are 25 terms

Hence the required sum

$\displaystyle \sf{ = \frac{25}{2} \bigg( 208 + 592\bigg)}$

$\displaystyle \sf{ = \frac{25}{2} \times 800}$

$\displaystyle \sf{ = 25\times 400}$

$= 10000$

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