Question

If the nth term of AP 9,7,5,.... is the same as the nth term of the AP 15,12,9...then find the value of n

Answer 1

Series 1: -  9 , 7,5,3.............
Difference = 2 = d
a = beginning term = 9
let t be the nth term 
Then t = a-(n-1)×d                          (- is because as it is in ascending order)
⇒ tn = 9-(n-1)×2          ........................  1
Series  2 : - 12,9,6,3
difference  =d= 3
Let t be the nth term 
t = a - (n-1) *d
tn = 12 - (n-1)* 3          ..........................2
eqn 1 = eqn 2
12 - (n-1)3 = 9 -(n-1)2
⇒ 3 = 3n - 3 -2n+2
⇒ 3 +3-2= n
⇒ n= 4                                       Ans.
I hope my answer is correct!
Thankyou!

Answer 2

For series 1,
a=9, d=-2

For series 2,
a=15, d=-3

an=a+(n-1)d

That is, 9+(n-1)*-2=15+(n-1)*-3
11-2n=18-3n

n = 7//