Question of RS Aggarwal book based on Arithmetic Progression For ICSE & CBSE Board Students.
Here the AP is given you have to find the value on which the n and the nth terms of AP are equal.
Question Number 21 Of Exercise 11A of RS Aggarwal Solution
Deepak BoraNewbie
For what value of n, the nth terms of arithmetic progression 63, 65,67,…..and 3,10,17,….are equal?
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In 1st AP:
Given AP is 63,65,67…..
First-term a = 63.
Common difference d = 65 – 63 = 2.
We know that sum of n terms an = a + (n – 1) * d
= 63 + (n – 1) * 2
= 63 + 2n – 2
= 61 + 2n ——- (1)
In 2nd AP :
Given AP is 3,10,17.
First-term a = 3.
Common difference d = 10 – 3 = 7.
We know that sum of n terms an = a + (n-1) d
= 3 + (n – 1) * 7
= 3 + 7n – 7
= 7n – 4 ——- (2)
Given that nth term of these AP are equal.
From (1) and (2),
we get
61 + 2n = 7n – 4
61 + 4 = 7n – 2n
61 + 4 = 5n
65 = 5n
n = 13.
Therefore 13th term of these AP’s are equal