Question

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

`a_1 = a_2 = 2, a_n = a_(n - 1) - 3, n > 2`

Answer 1

In the given problem, we are given the first, second term and the n^th term of an A.P.

We need to find its next five terms

`a_1 = 1, a_n = a_(n - 1) + 2, 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 tofind 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 = 3`  ....(2)

For `a_3` using n = 3 we get

`a_3 = a_(3 -1) + 2`

`a_3 = a_2 + 2`

`a_3 = 5`  ....(3)

For `a_4` usign n = 4 we get

`a_4 = a_(4 -1) + 2`

`a_4 = a_3 + 2`

`a_4 = 5 + 2`    (Using 3)

`a_4 = 7` ....(4)

For `a_5` using n = 5 we get

`a_5 = a_(5 -1) + 2`

`a_5 = a_4 + 2 `

`a_5 = 7 + 2`   (Using 4)

`a_5 = 9`  ....(5)

For `a_6` using n = 6 we get

`a_6 = a_(6 - 1) + 2`

`a_6 = a_5 + 2`

`a_6 = 9 + 2`  using 5)

a_6 = 11

Therefore, the next five terms, of the given A.P are `a_2 = 3, a_3 = 5, a_4 = 7, a_5 = 7, a_6= 11`