-5+(-8)+(-11)+....+(-230)

1.	-5+(-8)+(-11)+....+(-230)
Answer» –5 + (–8) + (–11) + …. + (–230)This is an AP.Here, a = –5d = –8 –(–5) = –8 + 5 = –3l = –230Let the number of terms of the AP be nWe know thatl = a + (n - 1)d{tex} \\Rightarrow {/tex}\xa0-230 = -5 + (n - 1) (-3){tex} \\Rightarrow {/tex}\xa0(n - 1) (-3) = -230 + 5{tex} \\Rightarrow {/tex}\xa0(n - 1) (-3) = -225{tex} \\Rightarrow n - 1 = \\frac{{ - 225}}{{ - 3}} = 75{/tex}{tex} \\Rightarrow {/tex}\xa0n = 75 + 1{tex} \\Rightarrow {/tex}\xa0n = 76Again, 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}\xa0S76 = 38(-235){tex} \\Rightarrow {/tex}\xa0S76 = -8930Hence, the required sum is -8930.

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