Q : 2     Find the sums given below :

            (iii)  \small -5+(-8)+(-11)+...+(-230)

Answers (1)

Given AP is 
\small -5+(-8)+(-11)+...+(-230)
We first need to find the number of terms
Here, a = -5 \ and \ a_n = -230
And
d = a_2-a_1=-8-(-5)= -3
Let suppose there are n terms in the AP
Now, we know that
a_n = a+(n-1)d
\Rightarrow -230 = -5 + (n-1)(-3)
\Rightarrow -228 = -3n
\Rightarrow n = 76
Now, we know that 
S = \frac{n}{2}\left \{ a+a_n \right \}
\Rightarrow S = \frac{76}{2}\left \{ (-5-230 )\right \}

\Rightarrow S = 38\left \{ -235\right \}
\Rightarrow S = -8930
Therefore, the sum of AP \small -5+(-8)+(-11)+...+(-230)   is -8930

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