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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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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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1. Given that,

Sn = 4nn2

First term, a = S1 = 4(1) − (1)2 = 4−1 = 3

Sum of first two terms = S2= 4(2)−(2)2 = 8−4 = 4

Second term, a2 = S2 − S1 = 4−3 = 1

Common difference, d = a2a = 1−3 = −2

Nth term, an = a+(n−1)

= 3+(n −1)(−2)

= 3−2n +2

= 5−2n

Therefore, a3 = 5−2(3) = 5-6 = −1

a10 = 5−2(10) = 5−20 = −15

Hence, the sum of first two terms is 4. The second term is 1.

The 3rd, the 10th, and the nth terms are −1, −15, and 5 − 2n respectively.

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