Question

If the n term of the

a.p. 9, 7, 5, ... is same as the th term of the

a.p. 15, 12, 9, ... find n.

Answer 1

☣ A.P↪ 9 , 7 , 5 ,..........

=> Given :- a ( first term ) = 9

d ( common difference ) = a2 - a1
= 7-9 = -2

So, we have to find nth term of A.P

=>an = a + ( n-1 )d

an = 9 + ( n-1) × (-2)

an = 9 -2n + 2

an = 7 - 2n ........( i )


Now,

☣ A.P↪ 15 , 12 , 9 ,.....

=> Given :- a = 15
d = -3

So, we have to find nth term of A.P.

=> an = a + ( n - 1 )d

an = 15 + ( n - 1 ) × (-3)

an = 15 -3n + 3

an = 18 - 3n ........ ( ii )

Now,

As given in the question that the value of an for both the equation is same

So,


an ( i ) = an ( ii )

7 - 2n = 18 - 3n

7 - 18 = - 3n + 2n

-11 = -n

11 =n


So, for the term of 11 both the A.P have the same number.



@Altaf

Answer 2

Answer:

• Required Value of n is 7.

Step-by-step explanation:

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.