The sum of nine consecutive odd numbers of Se | vedclass

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Question

(D) The average of the nine consecutive odd numbers is $\frac{621}{9} = 69$.Since there are nine numbers,the middle number (the $5$th number) is $69$.

Vedclass · Accepted Answer

$486$

Vedclass · Answer

(D) The average of the nine consecutive odd numbers is $\frac{621}{9} = 69$.Since there are nine numbers,the middle number (the $5$th number) is $69$.For consecutive odd numbers,the difference between consecutive terms is $2$. Thus,the smallest number of Set $A$ is $69 - (4 	imes 2) = 69 - 8 = 61$.The lowest number of the new set of six consecutive even numbers is $61 + 15 = 76$.The six consecutive even numbers are $76, 78, 80, 82, 84, 86$.The sum of these numbers is $\frac{n}{2}[2a + (n-1)d]$,where $n=6, a=76, d=2$.Sum $= \frac{6}{2}[2(76) + (6-1)2] = 3[152 + 10] = 3[162] = 486$.

The sum of nine consecutive odd numbers of Set $A$ is $621$. What is the sum of a different set of six consecutive even numbers whose lowest number is $15$ more than the lowest number of Set $A$?

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