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Question
Find the next five terms of the following sequences given by:
`a_1 = -1, a_n = (a_n - 1)/n, n>= 2`
Solution
`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`
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