Question

Find the AP, whose fourth term is 9 and sum of 6 and 13 term is 40

Answer 1

Answer:

3 , 5 , 7 , ................

Step-by-step explanation:

Given------> Fourth term of AP is 9 and sum of 6th and 13th term is 40 .

To find ------> Find the AP.

Solution-------> We know that, formula of nth term of AP be ,

aₙ = a + ( n - 1 ) d

Let , first term of AP be a and common difference be d.

ATQ, Fourth term of AP = 9

=> a₄ = 9

=> a + ( 4 - 1 ) d = 9

=> a + 3 d = 9

=> a = 9 - 3d

Now , ATQ,

a₆ + a₁₃ = 40

=> a + ( 6 - 1 ) d + a + ( 13 - 1 ) d = 40

=> a + 5 d + a + 12 d = 40

=> 2a + 17d = 40

Putting a = 9 - 3d , in it , we get,

=> 2 ( 9 - 3d ) + 17d = 40

=> 18 - 6d + 17d = 40

=> 11d = 40 - 18

=> 11d = 22

=> d = 22 / 11

=> d = 2

Now , a = 9 - 3d

Putting d = 2 in it we get,

=> a = 9 - 3 ( 2 )

=> a = 9 - 6

=> a = 3

First term = a = 3

Second term = a + d

= 3 + 2

= 5

Third term = a₂ + d

= 5 + 2

= 7

So AP is 3 , 5 , 7 , ................................