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Q : 11      If the sum of the first \small n terms of an AP is  \small 4n-n^2, what is the first term (that is  \small S_1)? What is the sum of first two terms? What is the second term? Similarly, find the \small 3rd, the \small 10th and the \small nth terms

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It is given that 
the sum of the first \small n terms of an AP is  \small 4n-n^2
Now,
\Rightarrow S_n = 4n-n^2
Now, first term is 
\Rightarrow S_1 = 4(1)-1^2=4-1=3
Therefore, first term is 3
Similarly,
\Rightarrow S_2 = 4(2)-2^2=8-4=4
Therefore, sum of first two terms is 4
Now, we know that
\Rightarrow S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_2 = \frac{2}{2}\left \{ 2\times 3+(2-1)d \right \}
\Rightarrow 4 = \left \{6+d \right \}
\Rightarrow d = -2
Now,
a_2= a+d = 3+(-2 )= 1
Similarly,
a_3= a+2d = 3+2(-2 )= 3-4=-1
a_{10}= a+9d = 3+9(-2 )= 3-18=-15
a_{n}= a+(n-1)d = 3+(n-1)(-2 )= 5-2n

 

Posted by

Gautam harsolia

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