What is the sum of all natural numbers between 100 and 200 formed by multiplying by 3 -

3 से गुना करके बनी 100 और 200 के बीच की सभी प्राकृत संख्याओं का योग क्या है -

Solution:

Natural numbers between 100 and 200 are formed by multiplying by 3 = 102,105,108,…….198.

Total number of terms from 102 to 198 = [Last term - First term / Common difference] +1

First term = 102

Last term = 198

Common difference = 105-102 = 3

Total number of terms n = [198 - 102/3] +1

= [96/3] +1

= 32+1

=33

Total number of terms n = 33

Sum of n natural numbers S_n = n/2[2a + (n − 1) × d]

= 33/2 [2 x 102 + (33-1) x 3]

= 33/2 [204 + 32 x 3]

= 33/2 [204 + 96]

= 33/2 [300]

= 33 x 150

= 4950

100 and 100 are obtained by multiplying by 3. The sum of natural numbers between 200 = 4950

So the correct answer is option B.

हल:

3 से गुणा करके बनी 100 और 200 के बीच की प्राकृत संख्यायें = 102,105, 108, …….198.

102 से 198 तक कुल पदों की संख्या = [अंतिम पद - प्रथम पद / सर्वान्तर] +1 

प्रथम पद = 102

अंतिम पद = 198

सार्वान्तर = 105-102 = 3 

कुल पदों की संख्या n = [198 - 102/3] +1

= [96/3] +1

= 32+1

=33

कुल पदों की संख्या n = 33

n प्राकृतिक संख्याओं का योग S_n = n/2[2a + (n − 1) × d]

= 33/2 [2 x 102 + (33-1) x 3]

= 33/2 [204 + 32 x 3]

= 33/2 [204 + 96]

= 33/2 [300]

= 33 x 150

= 4950

3 से गुणा करके बनी 100 और 200 के बीच की प्राकृत संख्याओं का योग = 4950

अतः सही उत्तर विकल्प B है l 

If the sum of two numbers is multiplied by those numbers separately, then the product comes to be 247 and 114 respectively. Accordingly, what is the sum of those numbers?

यदि दो संख्याओं के योग को उन संख्याओं से अलग-अलग गुणा की जाए, तो गुणनफल क्रमश 247 तथा 114 आता है । तदनुसार उन संख्याओं का योगफल कितना है ?