Question

Find the next five terms of the following sequences given by:

`a_1 = -1, a_n = (a_n - 1)/n, n>= 2`

Answer 1

`a_1 = -1, a_n = (a_n - 1)/n, n>= 2`

Here, we are given that `n >= 2`

So, the next five terms of this A.P would be `a_2, a_3, a_4` and `a_6`

Now `a_1 = 1` ......(1)

So to find the `a_2` term we use n = 2 we get

`a_2 = (a_2 -1)/2`

`a_2 = a_1/2`

`a_2 = (-1)/2`  (Using 1)

`a_2 = (-1)/2`    .....(2)

For `a_3` using n = 3 we get

`a_3 = (a_3 -1)/3`

` a_3 = a_2/3`

`a_3 = (-1/2)/3` ....(3)

For `a_4` using n = 4 we get

`a_4 = (a_4 -1)/4`

``a_4 = a_3/4``

`a_4 = (-1/6)/4` (Using 3)

`a_4 = (-1)/24`...(4)

For `a_5` using n = 5  we get

`a_5 = (a_5 - 1)/5`

`a_5 = (-1/24)/5`   (using 4)

`a_5 = (-1)/120`  .....(5)

For `a_6` using n = 6 we get

`a_6 = (a_6 - 1)/6`

`a_6 = a_5/6`

`a_6 = (-1/120)/6`   (Using 5)

`a_6 = (-1)/720`

Thereore the next five term of the given A.P are  `a_2 = (-1)/3, a_3 = (-1)/6,a_4 =(-1)/24,a_5 = (-1)/120, a_6 = (-1)/720`