Q : 5    The first term of an AP is \small 5, the last term is \small 45 and the sum is \small 400. Find the number of terms and the common difference.

Answers (1)

It is given that
\small a=5,a_n=45,S_n=400,
Now, we know that
a_n = a+(n-1)d
45 = 5+(n-1)d
(n-1)d= 40 \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)

Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow 400 = \frac{n}{2}\left \{ 2\times(5) +(n-1)d\right \}
\Rightarrow 800 = n\left \{ 10+40 \right \} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (using \ (i))
\Rightarrow 800 = n\left \{ 50 \right \}
\Rightarrow n = 16
Now, put this value in (i) we will get
d = \frac{40}{15}= \frac{8}{3}
Therefore, value of n and d are 16 \ and \ \frac{8}{3} respectively

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