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


The sum of first $n$ terms of an A.P. is $4n-n^{2}$.

To do:

We have to find the first term (that is $S_1$), sum of first two terms, second term, 3rd term, 10th term and the $n$th term. 


$S_{n} =4n-n^{2}$

For $n=1,\ S_{1} =4\times 1 -1^2=4-1=3$

Therefore, first term $a=3$

For $n=2,\ S_{2} =4\times 2-2^{2}=8-4=4$

$\therefore$ Second term of the A.P.$=S_{2} -S_{1}$



Common difference of the A.P., $d=$second term $-$ first term


We know that,








Therefore, the first term is $3$, the second term is $1$, the third term is $-1$, the tenth term is $-15$, $n$th term is $5-2n$ and the sum of the first two terms is $4$.


Simply Easy Learning

Updated on: 10-Oct-2022


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