Question

1. What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

Answer 1

The lowest number is 101 and the highest number is 998

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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