# Arithmetic Progressions

#### Answer:

In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of *n* terms of an A.P.,

Where; *a* = first term for the given A.P.

*d* = common difference of the given A.P.

*n *= number of terms

(i)

Common difference of the A.P. (*d*) =

So here,

First term (*a*) = 2

Last term (*l*) = 200

Common difference (*d*) = 2

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

On further simplification, we get,

Therefore, the sum of the A.P is

(ii)

Common difference of the A.P. (*d*) =

So here,

First term (*a*) = 3

Last term (*l*) = 803

Common difference (*d*) = 8

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 the A.P is

(iii)

Common difference of the ...

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