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The first term of an A.P. is $5$, the last term is $45$ and the sum of all the terms is $400$. Find the number of terms and the common difference of the A.P.
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$a = 5, a_n = 45, S_n = 400$
$\frac{n}{2}(5 + 45) = 400$
$\Rightarrow n = 16$
$5+15d=45$
$\Rightarrow d = \frac{40}{15} \text{ or } \frac{8}{3}$
$\frac{n}{2}(5 + 45) = 400$
$\Rightarrow n = 16$
$5+15d=45$
$\Rightarrow d = \frac{40}{15} \text{ or } \frac{8}{3}$