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
Given that 1 + 2 + 3 ... . + 10 = 55 , then what is ( 11 + 12 + 13 + ... . + 20 ) equal to ?
दिया गया है कि 1 + 2 + 3 ... . + 10 = 55 , तो ( 11 + 12 + 13 + ... . + 20 ) किसके बराबर है ?
What will be the product of three consecutive numbers whose sum is 15.
तीन क्रमागत संख्याओ का गुणनफल कितना होगा जिनका योगफल 15 है l