If the sum of the first n terms of an A.P. is 4n−n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Question

If the sum of the first n terms of an A.P. is 4n−n2, what is the first term (that is S1​)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Filo · Accepted Answer

If Sum of first n terms of an APSn​=4n−n2Then, the first term will be when n=1 in the above expressionS1​=a=4(1)−(1)2=3Sum of first two terms,n=2,S2​=4(2)−22=4So, the second term will be a2​=S2​−S1​=4−3=1Similarlyn=3,S3​=4(3)−32=3⇒a3​=S3​−S2​=3−4=−1n=9,S9​=4(9)−92=−45n=10,s10​=4(10)−(10)2=−60⇒a10​=S10​−S9​=−60−(−45)=−15an​=Sn​−S(​n−1)⇒an​=4n−n2−(4(n−1)−(n−1)2)⇒an​=5−2n

Question Text	If the sum of the first n terms of an $A . P$ . is $4 n - n^{2}$ , 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 $3 r d$ , the $10 t h$ and the nth terms.
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If the sum of the first n terms of an $A . P$ . is $4 n - n^{2}$ , 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 $3 r d$ , the $10 t h$ and the nth terms.

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Practice questions from similar books

If the sum of the first n terms of an A.P. is 4n−n2, what is the first term (that is S1​)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Text solutionVerified

Practice questions from similar books

If the sum of the first n terms of an $A . P$ . is $4 n - n^{2}$ , 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 $3 r d$ , the $10 t h$ and the nth terms.