Question

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

Answer 1

Consider the sequence defined by the recursive formula,

a1 = 2

a2 = 10

an = 2(an-1 + 2)/an-2

 

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

a1 = 2

a2 = 10

 

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

a3 = 2(a2 + 2)/a1

     = 2(10 + 2)/2

     = 2

 

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

a4 = 2(a3 + 2)/a2

     = 2(12 + 2)/10

     = 14/5

 

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

a5 = 2(a4 + 2)a3

     = 2(14/5 + 2)/12

     = (2 × 24/5)/12

     = 4/5

 

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

a6 = 2(a5 + 2)/a4

     = 2(4/5 + 2)/14/5

     = 2 × 14/14

     = 2

 

Compute seventh term of the sequence by substituting n = 7 in formula an = 2(an-1 + 2)/an-2,

a7 = 2(a6 + 2)/a5

     = 2(2 + 2)/4

     = 2 × 4/(4/5)

     = 10

 

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

a8 = 2(a7 + 2)/a6

     = 2(10 + 2)/2

     = 12

 

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

{2, 10, 12, 14/5, 4/5, 2, 10, 12}

The first eight terms of the given sequence are as follow:

{2, 10, 12, 14/5, 4/5, 2, 10, 12}