Question

find the sum of all three digit numbers which leave the same remainder 2 when divided by 5

Answer 1

Heya!

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Three digit numbers which leave the same remainder 2 when divided by 5 are -

102, 107 ... 997

a1 = 102
d = 5
l = 997

an = a + (n - 1) d

[ an = l ]

l = an = a + (n - 1) d

997 = 102 + (n - 1) 5

997 - 102 = 5n - 5
895 = 5n - 5

895 / 5 = n - 1

179 = n - 1
n = 179+1
n = 180


Now,

Sn = n/2 [ a + l ]
Sn = 180/2 [ 102 + 997 ]
Sn = 90 [ 1099 ]
Sn = 98,910

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Hope it helps...!!!