Question

the formula for nth term is a+[n-1]d.if 6th term is 10 and the 9th term is 13.then find 25th term

Answer 1

first ,find two equations then find the first term and tgen put all the values to get the 25th term

Answer 2

Given :- a6 = 10

a + ( n - 1 )d = 10

a + 5d = 10 ......... ( i )


a9 = 13

a + 8d = 13 ....... ( ii )


Sub ( ii ) from ( i )

a + 5d - ( a + 8d ) = 10 - 13

a + 5d - a - 8d = -3

- 3d = - 3

d = 1


Putting the value of d in equation ( i )


a + 5d = 10

a + 5 × 1 = 10

a + 5 = 10

a = 10 - 5

a = 5


Now

a25 = a + ( n - 1 )d

a25 = 5 + ( 24 - 1 )×1

a25 = 5 + 23

a25 = 28


So, the 25th term is 28