1. What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
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1. What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
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The AP is 101,104,107, ....... , 998
a = 101
d = 3
an = 998
n=number of terms = ?
Nth term of an AP(Arithmetic Progression) is given by
an=a+(n-1)d
998 = 101 + (n-1) 3
n-1 = 897/3
n = 299 + 1
n = 300
Sum to nth term in an AP is given by,
S=n/2(1st term + last term)
S = 300/2 (101 + 998 )
= 150 ( 1099 )
S= 164850
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