Sum of all two digit numbers which give a remainder of 4 when divided by 6 ?

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8. Sequences and Series

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What is the sum of all two digit numbers which give a remainder of $4$ when divided by $6$ ?

A

$777$

B

$776$

C

$780$

D

$784$

Solution

Such numbers are $10,16, \ldots . .94$

If $\mathrm{n}$ be the number of terms, then

$94=t_{n}=a+(n-1) d=10+(n-1) 6 \Rightarrow n=15$

$\therefore {\mathop{\rm sum}\nolimits} = \frac{{\rm{n}}}{2}({\rm{a}} + l) = \frac{{15}}{2}(10 + 94) = 780$

Standard 11

Mathematics

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