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

Answer:

The number of terms, n is 7.

Step-by-step explanation:

Given :  

Case : 1

Let the first term of this AP be 'A' , the common difference be 'D' and the nth term be 'An'.

A= 9, D = 7- 9 = - 2

 

Case : 2

Let the first term of this AP be 'a' , the common difference be 'd' and the nth term be 'an'

a = 15, d = 12 - 15 = -3

 

An = an            [Given]

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

3n - 2n = 18 - 11

n = 7  

Hence, the number of terms, n is 7.

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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.