-5+(-8)+(-11)+....+(-230)
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Sia ? 6 years, 4 months ago
–5 + (–8) + (–11) + …. + (–230)
This is an AP.
Here, a = –5
d = –8 –(–5) = –8 + 5 = –3
l = –230
Let the number of terms of the AP be n
We know that
l = a + (n - 1)d
{tex} \Rightarrow {/tex} -230 = -5 + (n - 1) (-3)
{tex} \Rightarrow {/tex} (n - 1) (-3) = -230 + 5
{tex} \Rightarrow {/tex} (n - 1) (-3) = -225
{tex} \Rightarrow n - 1 = \frac{{ - 225}}{{ - 3}} = 75{/tex}
{tex} \Rightarrow {/tex} n = 75 + 1
{tex} \Rightarrow {/tex} n = 76
Again, we know that
{tex}{S_n} = \frac{n}{2}(a + l){/tex}
{tex} \Rightarrow {S_{76}} = \frac{{76}}{2}\left[ {( - 5) + ( - 230)} \right]{/tex}
{tex} \Rightarrow {/tex} S76 = 38(-235)
{tex} \Rightarrow {/tex} S76 = -8930
Hence, the required sum is -8930.
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