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| 1. |
find the sum of (-5)+(-8)+(-11)+......+(-230) |
| Answer» (−5) + (−8)+ (−11) + ... + (−230) .Common difference of the A.P. (d) = a2\xa0- a1\xa0=-8-(-5)=-8+5=-3So here,First term (a) = −5Last term (l) = −230Common difference (d) = −3So, here the first step is to find the total number of terms. Let us take the number of terms as\xa0n.Now, as we know,an\xa0= a + (n-1) dSo, for the last term, - 230 = -5 + ( n-1) (-3)\xa0 - 230 = -5-3n + 3-23 +2 = -3n-228-3=n n = 76Now, using the formula for the sum of\xa0n\xa0terms, we getSn=762[2(-5)+(76-1)(-3)] = 38 [-10+(75)(-3)] =38 (-10-225) = 38(-235) = -8930Therefore, the sum of the A.P is Sn\xa0= -8930\xa0 | |