The best way to solve the problem of arithmetic progressions of exercise 5.3 of math for class 10th, what is the tricky way to solve this problem 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, the10th and the nth terms.

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# 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, the10th and the nth terms. Q.11

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Given that,

S= 4_{n}n−n^{2}First term,

a=S_{1}= 4(1) − (1)^{2}= 4−1 = 3Sum of first two terms =

S_{2}= 4(2)−(2)^{2}= 8−4 = 4Second term,

a_{2}=S_{2}−S_{1}= 4−3 = 1Common difference, d=a_{2}−a= 1−3 = −2N

^{th}term,a=_{n}a+(n−1)d= 3+(

n−1)(−2)= 3−2

n+2= 5−2

nTherefore,

a_{3}= 5−2(3) = 5-6 = −1a_{10}= 5−2(10) = 5−20 = −15Hence, the sum of first two terms is 4. The second term is 1.

The 3

^{rd}, the 10^{th}, and then^{th}terms are −1, −15, and 5 − 2nrespectively.