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Question 11
If the sum of the first n terms of an AP 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.
If the sum of the first n terms of an AP 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.
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Solution
Given that,Sn=4n−n2First term, a=S1=4(1)−(1)2=4−1=3Sum of first two terms=S2=4(2)−(2)2=8−4=4Second term, a2=S2−S1=4−3=1Common difference (d)=a2−a=1−3=−2
The nthterm of an A.P is given by
an=a+(n−1)d=3+(n−1)(−2)=3−2n+2=5−2nTherefore, a3=5−2(3)=5−6=−1a10=5−2(10)=5−20=−15Hence, the sum of first two terms is 4.The second term is 1.The 3rd,10th, and nth terms are −1,−15, and 5−2n respectively.
The nthterm of an A.P is given by
an=a+(n−1)d=3+(n−1)(−2)=3−2n+2=5−2nTherefore, a3=5−2(3)=5−6=−1a10=5−2(10)=5−20=−15Hence, the sum of first two terms is 4.The second term is 1.The 3rd,10th, and nth terms are −1,−15, and 5−2n respectively.
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