# The value of the expression 1-6+2-7+3-8+.........to 100 terms is

2
by vereashchander

2015-02-17T15:25:30+05:30
The answer is -250. I have attached the explanation.
2015-02-17T15:35:08+05:30

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(1+2+3+...50 terms)-(6+7+8...50 terms) ------------ equation
so now these are in ap
for (1+2+3+...50 terms) n=50, a=1 and d=1
by the formula Sn = n/2(2a+(n-1)d)
=50/2(2(1)+(50-1)1)
=25(51) ---------------------- 1
similarly for (6+7+8...50 terms) n=50, a=6, d=1
by placing this in formula we get 50/2(2(6)+(50-1)1)
= 25(12+49)
= 25(61) --------2
by adding 1 and 2 we get the value by the equation formed at first
= 25(51)-25(61)
= 25(51-61)
= 25(-10)
= -250
therefore, the value of given expression is -250