The nth term of an A.P is given by $(-4n+15)$. Find the sum of first $20$ terms of this A.P.

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The nth term of an A.P is given by $(-4n+15)$ . Find the sum of first $20$ terms of this A.P.

The nth term of an A.P is given by $(-4n+15)$ . Find the sum of first $20$ terms of this A.P.

As per the given information,

The n^th term of the A.P $=(-4n+15)$

So, by putting the value of n as $1$ and $20$ we can find the first and 20^th term of the A.P,

$a=(-4(1)+15)=11$

And,

${{a}_{20}}=\left( -4\left( 20 \right)+15 \right)=-65$

Now, for finding the sum of 20 terms of this A.P we have the first and last term as $a=11$ and ${{a}_{20}}=-65$

So, using the formula of sum of n terms of A.P

${{S}_{n}}=n/2\left( a+l \right)$

${{S}_{20}}=20/2\left( 11+\left( -65 \right) \right)$

$=10\left( -54 \right)$

$=-540$

Therefore, the sum of first 20 terms of this A.P. is $-540$ .

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