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14. find the sum of the odd numbers between
ol and 50. full explain
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The sum of the odd numbers between 0 and 50 is :
A. 525
B. 625
C. 425
D. 725
Answer
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Hint: The first odd number between 0 and 50 is 1 and the last odd number between 0 and 50 is 49. All the odd numbers between 0 and 50 are in AP having a common difference of 2. To solve this question, we will directly use the formula to find the sum of AP, given by, Sn=n2.{2a+(n−1)d} , where n = number of terms, a = first term and d = common difference.
Complete step-by-step answer:
It is given in the question that we have to find the sum of the odd numbers between 0 and 50. So, if we find the smallest odd number between 0 and 50, then it is 1 and the greatest odd number between 0 and 50 is 49. So, we have an AP of odd numbers between 0 and 50 with a common difference of 2. We will first try to find the total number of terms in the AP using the formula, Tn=a+(n−1)d , where Tn is the last term of the AP, a is the first term and d is the common difference. So, apply the formula, we get,
49=1+(n−1)2⇒49=1+2n−2⇒49=2n−1⇒2n=50⇒n=25
So, there are 25 terms in the given AP. Now, we can find the sum of the AP by suing the direct formula for the same, that is, Sn=n2.{2a+(n−1)d} , where n = number of terms, a = first term and d = common difference. So, we have n = 25, a = 1 and d = 2. So, applying these in the formula, we get,
Sn=252{2×1+(25−1)2}⇒Sn=252{2+24×2}⇒Sn=252{2+48}⇒Sn=25×502⇒Sn=25×25⇒Sn=625
Answer:
c
Step-by-step explanation:
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