Find the sum of all 2-digit numbers which leave a remainder 2 when they are divided by 6.

840

all 2-digit numbers which leave a remainder 2 when they are divided by 6 lying between 10 and 99 are,

14 , 20 , 26....................... , 98

Last term an = a + ( n - 1 )d

98 = 14 + ( n - 1)6

84 = ( n - 1 )6

n = 15

Sum of all the numbers , Sn = \(\frac{n}{2}\)( 2a + (n-1)d )

= \(\frac{15}{2}\)( 2 × 14 + 14 × 6)

= \(\frac{15}{2}\)(28 + 84)

= 840

The correct answer is Option (4) → 840