GATE2014-2-GA-4

Question

What is the average of all multiples of $10$ from $2$ to $198$?

• A. $90$
• B. $100$
• C. $110$
• D. $120$

Answer 1

$ a=10,l=190$

$ s=\dfrac{n(a+l)}{2}=\dfrac{19\times (200)}{2}=1900$

Average $=\dfrac{1900}{19}=100$

Ans. is 100

Correct Answer: $B$

Comments

It's an AP $10,20,.......190$

The average of an AP=$\frac{a_1+a_n}{2}=\frac{190+10}{2}$

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Average in case of A.P. series

average = (first + last) / 2
        =(190+10)/2 = 100

Answer 2

a=10

l=190

number of term=19

average of multiplae of 10= (n/2(2a+(n-1)d))/n

(2*10+18*10)/2=100

ans=100

Comments

Average in case of A.P. series
 
average = (first + last) / 2
        =(190+10)/2 = 100

Answer 3

10+20+30... + 180+190.

10(1+2+3+..19) Sum of first n no => n*(n+1)/2

(10*19*20)/2 = 1900.

Average = Sum / Total no = 1900/19 = (B) 100

Answer 4

b) 100

Answer 5

for finding average of any A.P. series just do
      (first term+last term)/2

in this question (10+190)/2 =100

Comments

Good Method