Q. 143.8( 10 Votes )

# If the n^{th} term of the A.P. 9, 7, 5,… is same as the nth term of the A.P. 15, 12, 9 … Find n.

Answer :

Given: n^{th} term of the A.P. 9, 7, 5,… is same as the nth term of the A.P. 15, 12, 9 …

We know, a_{n} = a + (n – 1)d where a is first term or a_{1} and d is common difference and n is any natural number

Let A.P. 9, 7, 5,… has first term a_{1} and common difference d_{1}

⇒ a_{1} = 9 and a_{2} = 7

Common difference, d_{1} = a_{2} – a_{1} = 7 – 9 = -2

Now, a_{n} = a_{1} + (n – 1)d_{1}

⇒ a_{n} = 9 + (n – 1)(-2)

⇒ a_{n} = 9 – 2n + 2

⇒ a_{n} = 11 – 2n

Let A.P. 15, 12, 9 … has first term a_{1} and common difference d_{1}

⇒ b_{1} = 15 and b_{2} = 12

Common difference, d_{2} = b_{2} – b_{1} = 12 – 15 = -3

Now, b_{n} = b_{1} + (n – 1)d_{2}

⇒ b_{n} = 15 + (n – 1)(-3)

⇒ b_{n} = 15 – 3n + 3

⇒ b_{n} = 12 – 3n

According to question:

a_{n} = b_{n}

⇒ 11 – 2n = 12 – 3n

⇒ 3n – 2n = 12 – 11

⇒ n = 1

Hence, the value of n is 1

Rate this question :

Find the second term and nth term of an A.P. whose 6^{th} term is 12 and 8^{th} term is 22.

There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.

RD Sharma - MathematicsIf x, y, z are in A.P. and A_{1}is the A.M. of x and y, and A_{2} is the A.M. of y and z, then prove that the A.M. of A_{1} and A_{2} is y.

Insert 7 A.M.s between 2 and 17.

RD Sharma - MathematicsThe 10^{th} and 18^{th} term of an A.P. are 41 and 73 respectively, find 26^{th} term.

If 10 times the 10^{th} term of an A.P. is equal to 15 times the 15^{th} term, show that the 25^{th} term of the A.P. is Zero.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P

RD Sharma - MathematicsThe 4^{th} term of an A.P. is three times the first and the 7^{th} term exceeds twice the third term by 1. Find the first term and the common difference.

In an A.P. the first term is 2, and the sum of the first 5 terms is one-fourth of the next 5 terms. Show that 20th term is - 112

RD Sharma - MathematicsInsert 4 A.M.s between 4 and 19.

RD Sharma - Mathematics