Question

If the sequence `(a - 3b)/b, (3a - 3b)/b, (5a - 3b)/b, (7a - 3b)/b,...` is an A.P. with common difference 3, then `a/b` = ______.

Answer 1

If the sequence `(a - 3b)/b, (3a - 3b)/b, (5a - 3b)/b, (7a - 3b)/b,...` is an A.P. with common difference 3, then `a/b` = `underlinebb(3/2)`.

Explanation:

Write the nth term: `t_n = ((2n - 1)a - 3b)/b` 

= `(2n - 1)(a/b) - 3`

So the common difference = t_{n + 1} – t_n 

= `2(a/b)` 

Set `2(a/b) = 3`

⇒ `a/b = 3/2`