What are the first term and the common differenceof an A.P. if the 2nd term is 5 and sixth term is 17?

Given that the second term is 5 and the 6th term is 17 in
an A.P.

Let the common difference be r and the first term
is a1.

Then we know that:

a2=
a1+ r

==> 5 = a1+
r...............(1)

Also we know
that:

a6 = a1+ 5r

==>
17 = a1+ 5r ..............(2)

Now we will solve the system
.

We will subtract (1) from
(2).

==> 12 =
4r

==> r= 3

Now we will
substitute into (1) to find a1.

==> 5= a1+
r

==> 5= a1+ 3 ==> a1= 5-3 =
2

Then the first term is a1=2 and the common
difference is r=3