Question

The sequence `(2a - 6b)/(3b), (2a - 3b)/(3b), (2a)/(3b), (2a + 3b)/(3b), (2a + 6b)/(3b)...` is an A.P. with common difference ______.

Answer 1

The sequence `(2a - 6b)/(3b), (2a - 3b)/(3b), (2a)/(3b), (2a + 3b)/(3b), (2a + 6b)/(3b)...` is an A.P. with common difference 1.

Explanation:

By definition the common difference d = a_{n + 1} – a_n. 

Compute one step: `((2a - 3b)/(3b)) - ((2a - 6b)/(3b))`

= `((2a - 3b) - (2a - 6b))/(3b)`

= `(3b)/(3b)`

= 1 

The next differences are the same, so the common difference is 1.