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