The sum of a series in A.P. is 525. Its first | vedclass

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(A) Let $n$ be the number of terms,$a$ be the first term,$l$ be the last term,and $d$ be the common difference.Given: $S_n = 525$,$a = 3$,$l = 39$.The

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$3/2$

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(A) Let $n$ be the number of terms,$a$ be the first term,$l$ be the last term,and $d$ be the common difference.Given: $S_n = 525$,$a = 3$,$l = 39$.The sum of an $A.P.$ is given by $S_n = \frac{n}{2}(a + l)$.Substituting the values: $525 = \frac{n}{2}(3 + 39)$.$525 = \frac{n}{2}(42) \Rightarrow 525 = 21n$.$n = \frac{525}{21} = 25$.Now,use the formula for the $n^{th}$ term: $l = a + (n - 1)d$.$39 = 3 + (25 - 1)d$.$39 - 3 = 24d$.$36 = 24d$.$d = \frac{36}{24} = \frac{3}{2}$.

The sum of a series in $A.P.$ is $525$. Its first term is $3$ and last term is $39$. Find the common difference.

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