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ICSE Class 10 Answered

FIND THE SUM OF ALL  ODD NO. LESS THAT 50 AND FIRST 12 NATURAL NUMBERS EACH OF WHICH IS A MULTIPAL OF 7

 

Asked by atanvi2006 | 22 May, 2021, 01:41: PM
Expert Answer
The first odd number is 1 and the last odd number is 49
The numbers 1, 3, 5, 7, ..., 49 forms an A.P. with a = 1 and d = 2
Let an = 49
a + (n - 1)d = 49
1 + (n - 1)2 = 49
Therefore, n = 25
Sum of n odd numbers is n2 
Therefore, sum of odd numbers less than 50 is 252 = 625
 
 
First 12 multiples of 7 are 7, 14, 21, ..., 84
This forms an A.P. with a = 7 and d = 7
Sum of n terms of an A.P. is given by
straight S subscript straight n equals straight n over 2 open square brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close square brackets
rightwards double arrow straight S subscript 12 equals 12 over 2 open square brackets 2 cross times 7 plus 11 cross times 7 close square brackets equals 6 open square brackets 14 plus 77 close square brackets equals 6 open parentheses 91 close parentheses equals 546
Answered by Renu Varma | 25 May, 2021, 11:42: AM

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