Question

Find the next five terms of the following sequences given by

a₁ = a₂ = 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

a₁ = a₂ = 2, a_n = a_n−1 − 3, n > 2

Here, we are given that n > 2

So, the next five terms of this A.P would be `a_3, a_4, a_5, a_6, a_7`

Now `a_1 = a_2 = 2` ....(1)

So, to find the `a_3`term we use n = 3  we get

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

`a_3 = a_2 - 3`

`a_3 = 2 - 3` (using 1)

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

For `a_4` using n = 4 we get

`a_4 = a_(4 -1) - 3`

`a_4 = a_3 - 3`

`a_4 = -1-3` (using 2)

`a_4 = -4` ....(3)

For `a_5` using n = 5 we get

`a_5 = a_(5 -1) - 3`

`a_5 = a_4 - 3`

`a_5 = -4 -3`  (Using 3)

`a_5 = -7` ...(4)

For `a_6` using n = 6 we get

`a_6 = a_(6 -1) - 3`

`a_6 = a_5 - 3`

`a_6 = -7 - 3` (Using 4)

`a_6  = -10` ......(5)

For `a_7` using n= 7 we get

`a_7 = a_(7 - 1) - 3`

`a_7 = a_6 - 3`

a_7 = -10 - 3 (Using 5)

`a_7 = -13`

Therefore, the next five terms, of the given A.P are

`a_3 = -1, a_4 = -4, a_5 = -7, a_6 = -10, a_7 = -13`