# Arithmetic Progressions

#### Answer:

(i) In this problem, we need to find the sum of all the multiples of 9 lying between 100 and 550.

So, we know that the first multiple of 9 after 100 is 108 and the last multiple of 9 before 550 is 549.

Also, all these terms will form an A.P. with the common difference of 9.

So here,

First term (*a*) = 108

Last term (*l*) = 549

Common difference (*d*) = 9

So, here the first step is to find the total number of terms. Let us take the number of terms as *n.*

Now, as we know,

So, for the last term,

Further simplifying,

Now, using the formula for the sum of *n* terms,

We get,

Therefore, the sum of all the multiples of 9 lying between 100 and 550 is

(ii)

In this problem, we need to find th...

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