In this Question the sum of first n terms of the AP is given. You have to find its nth term.
This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
This is the Question Number 24 Of Exercise 11 C of RS Aggarwal Solution
Deepak BoraNewbie
The sum of the first n terms of an AP is given by S_n=(2n^2+5n). Find the nth terms of the AP.
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Sum of first n terms of AP
S_n=2n^2+5n————-1st equation
n=1
by putting the value of n in the 1st equation
So,the First term is
2+5=7
now putting the value of n=2 to get the sum of two terms
=2×4+5×2
=18
This means first term + second term = 18
but first term =7
as calculated above so,
second term = 18-7 = 11
So
common difference becomes,
11-7 = 4
So the AP becomes, 7, 11, 15, ….nth term
= a + (n – 1)d
= 7 + (n-1)4
= 7 + 4n – 4
= 3 + 4n