Question

If 10th term is 9 and 9th term is 10, then the common difference is
O 1) d = -2
O2) d = -3
O3) d = 0
O4) d = -1​

Answer 1

Given

10th term is 9 and 9th term is 10

To Find

we have to find the common difference

$\sf\huge {\underline{\underline{{Solution}}}}$

Option 04) d= -1

Identity :an = a+(n-1)d

10th term can also be written as : a+(10-1)d= a+9d

9th term can also be written as:a+(9-1)d= a+8d

so,our equation becomes :

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

a+8d=10----(2)

substract Equation 1 from 2

=> a+8d-(a+9d)= 10-9

=> a+8d -a-9d= 1

=> 8d-9d= 1

=> -d = 1

d= -1

===========================================

Further solve :

from equation 1

=> a+9d = 9

=> a+9(-1)= 9

=> a-9= 9

=> a= 18

First term a= 18

second term = a+d= 18-1= 17

third term = a+2d= 18-2= 16

fourth term = a+3d= 18-3= 15

Fifth term = a+4d = 18-4= 14

Therefore, AP is 18,17,16,15,14-------∞

Answer 2

Answer:

Ans is option D

Step-by-step explanation:

Identity :an = a+(n-1)d

10th term can also be written as : a+(10-1)d= a+9d

9th term can also be written as:a+(9-1)d= a+8d

so,our equation becomes :

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

a+8d=10----(2)

substract Equation 1 from 2

=> a+8d-(a+9d)= 10-9

=> a+8d -a-9d= 1

=> 8d-9d= 1

=> -d = 1