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 first n terms of an A.P. is (3n^2 +7n)/2
then we have to find its nth term.
Also we have to write its 20th term.
CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 46
Given Sn = (3n2 + 7n) / 2,
On putting n = 1, we get the first term(a), S1 = a = [3(1)2 + 7(1)]/2 = 10/2 = 5
On putting n = 2 gives S2 = a + a + d = [3(2)2 + 7(2)]/2 = 26/2 = 13
=> d = 13 – 2a
=> d = 13 – 10 = 3
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
= 5 + (n – 1)3
= 5 + 3n – 3
= 3n + 2
Now we find the 20th term:
a20 = 3(20) + 2
= 60 + 2
= 62
Hence, the nth term of the given A.P. is 3n + 2 and the 20th term is 62