Question

Show that the sequence defined by an=5n - 7 is an A.P., find it's common difference.

Answer 1

we have, an = 5n - 7
put n = 1, we get a1 = 5(1) - 7 = 5 - 7 = - 2
put n = 2, we get a2 = 5(2) - 7 = 10 - 7 = 3
put n = 3 , we get a3 = 5(3) - 7 = 15 - 7 = 8
and so on.
we see that,
a2 - a1 = a3 - a2 = 5
So the sequence defined by an = 5n - 7 , is in AP.
Now common difference, d = 5