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Arithmetic Progressions

Answer:

(i) Here, we have an A.P. whose nth term (an), 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 (Sn).

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 nth term (an), sum of first n terms (Sn) 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 (Sn) = −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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