The first and last terms of an AP are 75 and | vedclass

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(B) Let the number of terms be $n$ and the common difference be $d$.Given,first term $a = 75$ and last term $l = a_n = 375$.The sum of an $AP$ is give

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$16, 20$

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(B) Let the number of terms be $n$ and the common difference be $d$.Given,first term $a = 75$ and last term $l = a_n = 375$.The sum of an $AP$ is given by $S_n = \frac{n}{2}(a + l)$.Substituting the values: $3600 = \frac{n}{2}(75 + 375)$.$3600 = \frac{n}{2}(450)$.$3600 = 225n$.$n = \frac{3600}{225} = 16$.Now,use the formula for the $n^{th}$ term: $a_n = a + (n - 1)d$.$375 = 75 + (16 - 1)d$.$375 - 75 = 15d$.$300 = 15d$.$d = \frac{300}{15} = 20$.Thus,the number of terms is $16$ and the common difference is $20$.

The first and last terms of an $AP$ are $75$ and $375$ respectively. If its sum is $3600$,find the number of terms in the $AP$ and its common difference.

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