The first four terms of sequence is 20, -10, -40, -70
Solution:
Given that we have to find the first four terms of sequence
Given recursive formula is:
[tex]a_n = 20 - 30(n-1)[/tex]
To find the first term, substitute n = 1
[tex]a_1 = 20-30(1-1)\\\\a_1 = 20-30(0)\\\\a_1 = 20[/tex]
Thus the first term of sequence is 20
To find the second term, substitute n = 2
[tex]a_2 = 20-30(2-1)\\\\a_2 = 20-30(1)\\\\a_2 = 20-30\\\\a_2 = -10[/tex]
Thus the second term of sequence is -10
To find the third term, substitute n = 3
[tex]a_3 = 20-30(3-1)\\\\a_3 = 20-30(2)\\\\a_3 = 20-60\\\\a_3 = -40[/tex]
Thus the third term of sequence is -40
To find the fourth term, substitute n = 4
[tex]a_4 = 20-30(4-1)\\\\a_4 = 20-30(3)\\\\a_4 = 20-90\\\\a_4 = -70[/tex]
Thus the first four terms of sequence is 20, -10, -40, -70
