This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been given that The sum of the first n terms of an A.P. is 5n – n2.
Now we have to Find the nth term of this A.P.
CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 39
Given Sn = 5n – n2,
On putting n = 1, we get the first term(a), S1 = a = 5(1) – (1)2 = 4
On putting n = 2 gives S2 = a + a + d = 5(2) – (2)2 = 6
=> d = 6 – 2a
=> d = 6 – 8 = –2
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
= 4 + (n – 1)(–2)
= 4 – 2n + 2
= 6 – 2n
Hence, the nth term of the given A.P. is 6 – 2n.