Prove that no matter what is the real number a and b are, the sequence with nth term a+nb is always an A.P. What is the common difference?
Put n = 1
A1= a + b
Put n = 2
A2= a + 2b
Put n = 3
A3= a + 3b
Put n = 4
A4= a + 4b
Common difference, d1 = a2 – a1 = a + 2b – a – b = b
Common difference, d2= a3 – a2 = a+ 3b – a – 2b = b
Common difference, d3 = a4 – a3 = a+ 4b – a – 3b = b
Since, d1 = d2 = d3
Therefore, it’s an A.P. with common difference ‘b’