Question

Which recursive sequence would produce the sequence 8, -20,64. ...? a = 8 and an = -3an-1 + 4 a = 8 and an = 4an-1-3 a = 8 and an 8 and an = -4an- 1 - 2 a 8 and an = -2a,- 1 - 4

Answer 1

Given sequence is 8, -20, 64, .......

To understand which options is correct, let's evaluate all the options.

Option 1:

a = 8

an = -3a(n-1) + 4

To find second term, put n = 2

a2 = -3a(2-1) + 4

a2 = -3a1 + 4

a2 = -3(8) + 4 ()a = a1

a2 = -24 + 4

a2 = -20 ()That is the correct second term

now, lets put n = 3, we get

a3 = -3a(3-1) + 4

a3 = -3a2 + 4

a3 = -3(-20) + 4

a3 = 60 + 4

a3 = 64 (that is the correct third term)

Hence, this option is correct.

Similarly, you can evaluate other options but that will result in a false sequence. For example, take option 2.

a = 8

an = 4a(n-1) - 3

a2 = 4a1 - 3

a2 = 4(8) - 3

a2 = 21. (this is not the correct term)

hence, this option is wrong