Question

For the following exercises, write the first eight terms of the sequence.

Answer 1

Consider the sequence defined by the recursive formula,

a1 = -1

a2 = 5

an = an-2(3 – an-1)

 

First two terms of the sequence are provided in the formula as follow:

a1 = -1

a2 = 5

 

Compute third term of the sequence by substituting n = 3 in formula an = an-2(3 – an-1)

a3 = a1(3 – a2)

      = -1(3 – 5)

     = -1(-2)

     = 2

 

Compute forth term of the sequence by substituting n = 4 in formula an = an-2(3 – an-1)

a4 = a2(3 – a3)

     = 5(3 - 2)

     = 5(1)

     = 5

 

Compute fifth term of the sequence by substituting n = 5 in formula an = an-2(3 – an-1),

a3 = a3(3 – a4)

     = 2(3 – 5)

     = 2(-2)

     = -4

 

Compute sixth term of the sequence by substituting n = 6 in formula an = an-2(3 – an-1)

a6 = a4(3 – a5)

     = 5[3 –(-4)]

     = 5(7)

     = 35

 

Compute seventh term of the sequence by substituting n = 7 in formula

an = an-2(3 – an-1),

 

Therefore,

a7 = a5(3 – a6)

     = -4(3 – 35)

     = -4(-32)

     = 128

 

Compute 8th term of the sequence by substituting n = 8 in formula an = an-2(3 – an-1),

a8 = a6(3 – a7)

     = 35(3 – 128)

     = 35(-125)

     = -4375

 

Therefore, the first eight terms of the given sequence are as follow:

{-1, 5, +2, +5, -4, +35, +128, -4375}

Therefore, the first eight terms of the given sequence are as follow:

{-1, 5, +2, +5, -4, +35, +128, -4375}.