Q : 2     Find the sums given below :

            (ii)    \small 34+32+30+...+10

Answers (1)

Given AP is 
\small 34+32+30+...+10
We first need to find the number of terms
Here, a = 34 \ and \ a_n = 10
And
d = a_2-a_1=32-34=-2
Let suppose there are n terms in the AP
Now, we know that
a_n = a+(n-1)d
\Rightarrow 10 = 34 + (n-1)(-2)
\Rightarrow -26 = -2n
\Rightarrow n = 13
Now, we know that 
S = \frac{n}{2}\left \{ a+a_n \right \}

\Rightarrow S = \frac{13}{2}\left \{ 44\right \}
\Rightarrow S =13\times 22 = 286
Therefore, the sum of AP \small 34+32+30+...+10   is 286

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