Notifications
Clear all
Arithmetic Progressions
1
Posts
2
Users
0
Likes
252
Views
0
31/05/2021 11:46 am
Topic starter
For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?
1 Answer
0
31/05/2021 11:48 am
Given two APs as; 63, 65, 67,… and 3, 10, 17,….
Taking first AP,
63, 65, 67, …
First term, a = 63
Common difference, d = a2−a1
= 65−63 = 2
We know, nth term of this A.P. = an = a+(n−1)d
an= 63+(n−1)2 = 63+2n−2
an = 61+2n ………………. (i)
Taking second AP,
3, 10, 17, …
First term, a = 3
Common difference, d = a2 − a1
= 10 − 3 = 7
We know that,
nth term of this A.P.
= 3+(n−1)7
an = 3+7n−7
an = 7n−4 ……………….. (ii)
Given, nth term of these A.P.s are equal to each other.
Equating both these equations, we get,
61+2n = 7n−4
61+4 = 5n
5n = 65
n = 13
Therefore, 13th terms of both these A.P.s are equal to each other.