Q : 1     Find the sum of the following APs:

             (i)    \small -37,-33,-29,..., to \small 12 terms.

Answers (1)

Given AP is 
\small -37,-33,-29,..., to \small 12 terms.
Here, a = -37 \ and \ n = 12
And
d = a_2-a_1=-33-(-37)=4
Now, we know that 
S = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S = \frac{12}{2}\left \{ 2\times (-37) +(12-1)4\right \}
\Rightarrow S = 6\left \{ -74 +44\right \}
\Rightarrow S = 5\left \{ -30\right \}
\Rightarrow S =-180
Therefore, the sum of AP  \small -37,-33,-29,..., to \small 12 terms. is -180

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