Question

If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.

Answer 1

Solution:

It is given that nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9,. It means Tn = Pn.

By Given Condition, We have:

• Tn = a + ( n -1)d
• Tp = a + ( n -1)d

⇒ Tn = Tn

⇒ a + ( n -1)d = a + ( n-1)d

⇒ 9 + ( n - 1)-2= 15 + ( n -1)-3

⇒ 9 - 2n + 2 = 15 - 3n + 3

⇒ 11- 2n = 18 - 3n

⇒ 11 - 18 = -3n + 2n

⇒ - 7 = - n

⇒ n = 7

•°• Therefore, Required Value of n is 7.

Answer 2

Step-by-step explanation:

Given,

nth term of A.P. 9,7,5... is same as the nth term of the A.P. 15,12,9...

From the First A.P.,

a = 9 , d = 7-9 = -2

From the Second A.P.,

a1 = 15 , d = 12-15 = -3

Now,

nth term of 1st AP = nth term of 2nd AP

an = an

a+(n-1)d = a1+(n-1)d

9+(n-1)-2 = 15+(n-1)-3

9-2n+2 = 15-3n+3

11-2n = 18-3n

-2n+3n = 18-7

n = 7

Therefore, n = 7

Hope it helps