This is the basic and conceptual 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 3n2 + 6n.
Now we have to Find the nth term of this A.P.
CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 38
Given Sn = 3n2 + 6n
On putting n = 1, we get the first term(a), S1 = a = 3(1)2 + 6(1) = 9
On putting n = 2 gives S2 = a + a + d = 3(2)2 + 6(2) = 24
=> d = 24 – 2a
=> d = 24 – 18 = 6
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
= 9 + (n – 1)6
= 9 + 6n – 6
= 6n + 3
Hence, the nth term of the given A.P. is 6n + 3.