Question

Find the first five terms of the recursive sequence.

Answer 1

The first five terms of sequence is 4.5, -27, 162, -972, 5832

Solution:

Given that we have to find first five terms of recursive sequence

Given sequence is:

`a_n = -6a_(n - 1)`

To find first five terms, substitute n = 2, 3, 4, 5

First term is given =
`a_1` = 4.5

Find second term:

Substitute n = 2 in given sequence

`a_2 = -6a_(2 - 1)\\\\a_2 = -6a_1\\\\a_2 = -6(4.5) = -27`

Thus second term of given sequence is -27

Find third term:

Substitute n = 3 in given sequence

`a_3 = -6a_(3-1)\\\\a_3 = -6a_2\\\\a_3 = -6(-27) = 162`

Thus third term of given sequence is 162

Find fourth term:

Substitute n = 4 in given sequence

`a_4 = -6a_(4-1)\\\\a_4 = -6a_3\\\\a_4 = -6(162) = -972`

Thus fourth term of given sequence is -972

Find fifth term:

Substitute n = 5 in given sequence

`a_5 = -6a_(5-1)\\\\a_5 = -6a_4\\\\a_5 = -6(-972) = 5832`

Thus the first five terms of sequence is 4.5, -27, 162, -972, 5832