Question

If 3 times the third term of an A.P. is equal to 5 times the fifth term then 8th term is

Answer 1

Third term of an A.p means (a+2d) (equation 1)

and 5term means (a+4d) (equation 2)

a+2d=a+4d

a-a=4d-2d

2d=0

d= -2

putting the value of d in equation 1 you can also put the value of d in equation 2

i.e a+2d=0

a+2×-2=0

a+(-4)=0

a-4=0

a=4

Now,the A.p is 4,2,0,-2...

n=8

an= a+(n-1)d

= 4+(8-1)-2

=4+(7)-2

=4-14

= -10

Answer 2

Answer:

Let say first term of an AP = a

Let say common difference of AP = d

Third term of an AP = a + 2d

Fifth term of an AP = a + 4d

3 × Third term = 5 × Fifth Term

=> 3 × (a+2d) = 5 ×(a + 4d)

=> 3a + 6d = 5a + 20d

=> 0 = 2a + 14d

dividing by 2 both sided

=> 0 = a + 7d

=> a + 7d = 0

8th term of AP = a + 7d

from above equation

8th term = 0

Step-by-step explanatio