Question

+ 5) Consider the sequence of two digit numbers which leave a remainder 1 on division by 2
a) What is the common difference?
b) Which is the smallest number in this sequence? c) How many two digit numbers are there which leave remainder 1 on division by 2?
d) What is the sum of such numbers?​

Answer 1

Answer:

When a no. is divided by 2 it leaves remainder 0 or 1.

0 if it is even and 1 if it is odd.

So the question is no. of two digit odd no.s.

A simple way to count is using formula of nth term of AP i.e. an = a+ (n-1)d.

d=2(common difference)

a=11(first term)

an=(nth term not a*n) which is 99.

We conclude that there are 45 such no.s.

But if we consider negative numbers also then answer is 90.