Question

the difference between 5th and 9th term of an arithmetic sequence is 20.what is the difference between its 1st and 3rd terms?​

Answer 1

Answer:

Let a be the 1st term of A.P and d be its common difference .

From general term formula of an A.P

an=a+(n-1)d

So, 5th term =a+(5-1)d=a+4d

and 9th term= a+(9-1)d= a+8d

Now , difference b/w 5th term and 9th term is

=a+4d-a-8d=-4d and -4d=20 (given)

So, common difference =d= -5.

Now , difference b/w 1st term and 3rd term is

=a-[a+(3-1)d]=a-a-2d = -2d =-2(-5)= 10.