Q. 84.7( 3 Votes )

# The 6^{th} and 17^{th} terms of an A.P. are 19 and 41 respectively. Find the 40^{th} term.

Answer :

Given,

6^{th} term of an A.P is 19 and 17^{th} terms of an A.P. is 41

⇒ a_{6} = 19 and a_{17} = 41

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

When n = 6:

∴ a_{6} = a + (6 – 1)d

⇒ a_{6} = a + 5d

Similarly, When n = 17:

∴ a_{17} = a + (17 – 1)d

⇒ a_{17} = a + 16d

According to question:

a_{6} = 19 and a_{17} = 41

⇒ a + 5d = 19 ………………(i)

And a + 16d = 41…………..(ii)

Subtracting equation (i) from (ii):

a + 16d – (a + 5d) = 41 – 19

⇒ a + 16d – a – 5d = 22

⇒ 11d = 22

⇒ d = 2

Put the value of d in equation (i):

a + 5(2) = 19

⇒ a + 10 = 19

⇒ a = 19 – 10

⇒ a = 9

As, a_{n} = a + (n – 1)d

a_{40} = a + (40 – 1)d

⇒ a_{40} = a + 39d

Now put the value of a = 9 and d = 2 in a_{40}

⇒ a_{40} = 9 + 39(2)

⇒ a_{40} = 9 + 78

⇒ a_{40} = 87

Hence, 40^{th} term of the given A.P. is 87

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