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Test by Bikram | Mock GATE | Test 2 | Question: 64
Bikram
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The value of the expression $1 - 6 + 2 - 7 + 3 - 8 +$……… to $100$ terms is __________.
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This series can be written as
(1 + 2 + 3 + ......to 50 terms) - (6 + 7 + 8 + .....to 50 terms)
Both these are in AP’s
a =1, n =50, d= 1 for first series
a= 6, n =50 , d= 1 for second series
using AP formula n/2[ 2a + (n-1)d ] the 100th term is -250
Bikram
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Lakshman Bhaiya
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Sum of $AP $, if the last term is given, then $S_{n} = \frac{n}{2}(a+l)$ Where $a=$first term, $l=$last term, $n=$total number of terms.
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Just group each 2 numbers from left hand side. Summation of each 2 numbers will give -5 here.
(1-6)+(2-5)+(3-8)+....upto 50 terms.(as we grouped 2 numbers each time)
=-5-5-5-...50 terms
=-5*50= -250
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Answer:
-250
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