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:
[tex]a_n = -6a_{n - 1}[/tex]
To find first five terms, substitute n = 2, 3, 4, 5
First term is given = [tex]a_1[/tex] = 4.5
Find second term:
Substitute n = 2 in given sequence
[tex]a_2 = -6a_{2 - 1}\\\\a_2 = -6a_1\\\\a_2 = -6(4.5) = -27[/tex]
Thus second term of given sequence is -27
Find third term:
Substitute n = 3 in given sequence
[tex]a_3 = -6a_{3-1}\\\\a_3 = -6a_2\\\\a_3 = -6(-27) = 162[/tex]
Thus third term of given sequence is 162
Find fourth term:
Substitute n = 4 in given sequence
[tex]a_4 = -6a_{4-1}\\\\a_4 = -6a_3\\\\a_4 = -6(162) = -972[/tex]
Thus fourth term of given sequence is -972
Find fifth term:
Substitute n = 5 in given sequence
[tex]a_5 = -6a_{5-1}\\\\a_5 = -6a_4\\\\a_5 = -6(-972) = 5832[/tex]
Thus the first five terms of sequence is 4.5, -27, 162, -972, 5832
