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Find the mean of the first five multiples of 3.

Find the mean of the first five multiples of 3.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
22 days ago
Hint: : For solving this problem we need to generalise the equation of mean for first ′n′ multiples of 3 and then we substitute n=5 to get the required mean. We find the mean of data using the formula mean=sum of all the numbersnumber of numbers . Complete step-by-step solution: Let us assume that there are ′n′ multiples of 3. So, we can say that the number of multiples is ′n′ Now, let us find the sum of first ′n′ multiples of 3 as follows ⇒Sn=3(1)+3(2)+3(3)+.......+3(n) By converting the above equation to summation we will get ⇒Sn=∑3n⇒Sn=3∑n We know that the formula of first ′n′ natural numbers as ∑n=n(n+1)2 By substituting this result in above equation we will get ⇒Sn=3(n(n+1)2)⇒Sn=3n(n+1)2 Here, we got the sum of first ′n′ multiples of 3. But, we are asked to find the sum of the first five multiples of 3. By substituting n=5 in above result we get ⇒S5=3(5)(5+1)2⇒S5=45 Let us assume that the mean of the first five multiples of 3 as X . We know that the formula of mean is given as mean=sum of all the numbersnumber of numbers By substituting the required numbers in above formula we get ⇒X=S5n⇒X=455⇒X=9 Therefore the mean of the first five multiples of 3 is 9. Note: This problem can be solved in another method. We know that the first five multiples of 3 are 3, 6, 9, 12, 15. Let us find the sum of numbers as ⇒S=3+6+9+12+15⇒S=45 Here, there are 5 numbers. Let us assume that the mean of the first five multiples of 3 as X . We know that the formula of mean as mean=sum of all the numbersnumber of numbers By substituting the required numbers in above formula we get ⇒X=Sn⇒X=455⇒X=9 Therefore the mean of the first five multiples of 3 is 9.

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