# Arithmetic Progressions

#### Answer:

(i) Here, we have an A.P. whose *n*^{th} term (*a*_{n}), first term (*a*) and common difference (*d*) are given. We need to find the number of terms (*n*) and the sum of first *n* terms (*S*_{n}).

Here,

First term (*a*) = 5

Last term () = 50

Common difference (*d*) = 3

So here we will find the value of *n* using the formula,

So, substituting the values in the above mentioned formula

Further simplifying for *n*,

Now, here we can find the sum of the *n* terms of the given A.P., using the formula,

Where, *a* = the first term

*l* = the last term

So, for the given A.P, on substituting the values in the formula for the sum of *n* terms of an A.P., we get,

Therefore, for the given A.P

(ii) Here, we have an A.P. whose *n*^{th} term (*a*_{n}), sum of first *n* terms (*S*_{n}) and common difference (*d*) are given. We need to find the number of terms (*n*) and the first term (*a*).

Here,

Last term () = 4

Common difference (*d*) = 2

Sum of *n* terms (*S*_{n}) = −14

So here we will find the value of *n* using the formula,

So, substituting the values in the above mentioned formula

Now, here the sum of the *n* terms is given by the formula,

Where, *a* = the first term

*l* = the last term

So, for the given A.P, on substituting the values in the formula for the sum of *n* terms of an A.P., we get,

Equating (1) and (2), we get,

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