After inserting n arithmetic means (A.M.s) be | vedclass

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(B) The resulting progression consists of $n + 2$ terms,where the first term $a = 2$ and the last term $l = 38$.The sum of an arithmetic progression i

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$8$

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(B) The resulting progression consists of $n + 2$ terms,where the first term $a = 2$ and the last term $l = 38$.The sum of an arithmetic progression is given by the formula $S_m = \frac{m}{2}(a + l)$,where $m$ is the total number of terms.Here,$m = n + 2$,$a = 2$,and $l = 38$.Given that the sum is $200$,we have:$200 = \frac{n + 2}{2}(2 + 38)$$200 = \frac{n + 2}{2}(40)$$200 = 20(n + 2)$Dividing both sides by $20$:$10 = n + 2$$n = 10 - 2 = 8$.Therefore,the value of $n$ is $8$.

After inserting $n$ arithmetic means $(A.M.s)$ between $2$ and $38$,the sum of the resulting progression is $200$. The value of $n$ is

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