Average

Hi,
Average of an Arithmetic series(progression) is always the average of first term and last term.
So, Avg = (10+400)/2 = 205.

Hence, D

If shortcut does not click
Total no of multiples : (400-10)/10 + 1 = 40
Sum of A.P. = 410*20
Average = 410*20/40 =205

IMO D

There is a short cut formula :

Number of terms in between 2 numbers : [(Last Term-First Term)/ Incremental]+1
Sum of Number of Terms : ([Last Term+First Term)/2]* number of terms


10+20+30+....+400 =

step 1: ((400-10)/10)+1 : 40
step 2: ((400+10)/2)*40 : 8200

8200/40 = 205

Many answers already, but if you're not a formula junkie:
10+400 = 410 (1st term)
20+390 = 410 (2nd term)
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.
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200+210 = 410 (20th term)

The sum of all the 20 terms mentioned above is the same as the sum of all the 40 multiples of 10 between 10 and 400 (both inclusive)

Hence the average is (20x 410)/40 = 205

s = 10+20+30+40+....+400
Arithmetic progression series
no. of terms = 40
to find s/40
a is the first term = 10
l is last term = 400
thus sum = (n/2)*(a+l)
to find avg, or sum/n = (400+10)/2 = 410/2 = 205
IMO D

205 is the ans.its an ap sereis where avg is the average of first and last term