Question

In an ap the 9th term is -4 times the fourth term and the sum of the 5th and 7th terms is 9 . find the first term and the common difference.​

Answer 1

I) A+8D= -4(A+3D)

A+8D= -4A-12D

5A = -20D

A=-4D

II)  A+4D+A+6D=9

     2A+10D=9

      -8D+10D=9  (A=-4D)

      D=9/2

         =4.5

First Term=A=-4D

                     =-4*4.5

                      =-18

Thus Answer is -18 and 4.5.

                 

Answer 2

Answer:

First term is - 18 and common difference is 9/2.

Step-by-step explanation:

In AP, nth term = a + ( n - 1 )d, where a is the first term and d is the common difference.

Let first term of this AP be a and commom difference be d.

According to question:

= > 9th term = - 4 * 4th term

= > a + 8d = - 4( a + 3d )

= > a + 8d = - 4a - 12d

= > a + 4a = - 12d - 8d

= > 5a = - 20d

= > a = - 4d ... (1)

= > 5th + 7th term = 9

= > a + 4d + a + 6d = 9

= > 2a + 10d = 9

= > 2( - 4d ) + 10d = 9 { from (1) }

= > - 8d + 10d = 9

= > 2d = 9

= > d = 9/2

Hence, a = - 4(9/2) = - 2(9) = - 18