Question

prove that the sum of all two digits number which are divisible by 3 is 1665.​

Answer 1

Answer:

Here is prove:

Step-by-step explanation:

First two digit number divisible by 3 = 12

Last two digit number divisible by 3 = 99

∴ First term, (a)=12

Common difference, (d)=3

Last term, (l)=99

n=?

As we know that,

an=a+(n−1)d

∴99=12+(n−1)3

⇒(n−1)387

⇒n=29+1=30

∴ Sum of n terms of an A.P., when last term is known is given by-

Sn=2n(a+l)

∴S30=230(12+99)

⇒S30=15×111=1665