Question

Show that the sequence defined by a_n =5n-7 is an A.P ,find its common differnce

Answer 1

we have, a_n = 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 a_n = 5n - 7 , is in AP.
Now common difference, d = 5