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.
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.

Solution:

Provided here that,

Sn = 4nn2

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

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

The second term, a2 = S2 − S1 = 4−3 = 1

The common difference, d = a2a = 1−3 = −2

Nth term, an = a+(n−1)

= 3+(n −1)(−2)

= 3−2n +2

= 5−2n

As a result, a3 = 5−2(3) = 5-6 = −1

a10 = 5−2(10) = 5−20 = −15

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

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