alleryThe first term of an AP is $5$, the last term is $45$ and the sum is $400$. Find the number of terms and the common difference.
A$n=16,\ d=\frac{8}{3}$
B$n=20,\ d=2$
C$n=18,\ d=\frac{5}{2}$
D$n=15,\ d=3$
Answer & Solution
Correct answer: A. $n=16,\ d=\frac{8}{3}$
Use the sum formula with first and last terms: $S=\frac{n}{2}(a+l)$. So
$$400=\frac{n}{2}(5+45)=25n,$$
which gives $n=16$. Then using $l=a+(n-1)d$,
$$45=5+15d \Rightarrow 15d=40 \Rightarrow d=\frac{8}{3}.$$
So the AP has 16 terms and common difference $\frac{8}{3}$.
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