Find the sum of all positive multiples of 3 less than 50-
50 से कम 3 के सभी धनात्मक गुणजो का योग ज्ञात कीजिये-
Solution:
I Method:
All positive multiples of 3 less than 50 = 3, 6, 9, 12, 15 ......, 48
First term = 3
Last term = 48
Difference = 6-3=3
Total number of multiples of 3 less than 50 (n) = [(last number - first number)/difference] +1
n = [(48-3)/ 3] +1
n = [45/ 3] +1
n = 15+1
n = 16
Sum of all positive multiples Sn = n/2[2a + (n − 1) × d]
= 16/2 [2 x 3 + (16-1) x 3]
= 8 [6 + 15 x 3]
= 8 [6+45]
= 8 x 51
= 408
II Method:
All positive multiples of 3 less than 50 = 3, 6, 9, 12, 15 ......, 48
= 3 (1,2,3,4,....16)
Sum of n natural numbers = n(n+1)/2
(1,2,3,4,....16)
= 16(16+1)/2
= 8 x 17
= 136
Hence, sum = 3 x 136
= 408
The sum of multiples of 3 less than 50 = 408
Hence, the correct answer is option C.
हल:
I Method:
प्रथम पद = 3
अंतिम पद = 48
सार्वांतर = 6-3=3
50 से कम 3 के गुणजो की कुल संख्या n = [(अंतिम संख्या - प्रथम संख्या)/सार्वांतर] +1
n = [(48-3)/ 3] +1
n = [45/ 3] +1
n = 15+1
n = 16
सभी धनात्मक गुणजो का योगफल Sn = n/2[2a + (n − 1) × d]
= 16/2 [2 x 3 + (16-1) x 3]
= 8 [6 + 15 x 3]
= 8 [6+45]
= 8 x 51
= 408
II Method:
50 से कम 3 के सभी धनात्मक गुणज = 3, 6, 9, 12, 15 ......, 48
= 3 (1,2,3,4,....16)
n प्राकृतिक संख्याओं का योग = n(n+1)/2
(1,2,3,4,....16)
= 16(16+1)/2
= 8 x 17
= 136
अतः योग = 3 x 136
= 408
50 से कम 3 के गुणजो का योग = 408
अतः सही उत्तर विकल्प C है l
If the sum of seven consecutive even integers is 140, then what is the largest even integer among them?
यदि सात क्रमिक सम पूर्णांकों का योग 140 है तो इनमे से सबसे बड़ा सम पूर्णांक क्या है ?
