Test by Bikram | Mock GATE | Test 2 | Question: 64

Question

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

Answer 1

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

Comments

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.

Answer 2

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