Need some help please

Question

Write the first five terms of the geometric sequence.
a1=4, r=-1/square root of 2

Answer 1

Justin,

In math, a geometric sequence (a_n), is a sequence of numbers where each term after the first one is computed by multiplying the previous term by a fixed, non-zero number (r) called the common ratio. 

 

Thus term a_k = r a_(k-1).   for k = 2, 3,  ...      and a₁ is given to start of the sequence.

 

In your problem:  a₁ = 4   and r = -1/√2  = - 0.7071.  So the first five terms of this geometric sequence are:

 

a₁ =  +4

a₂ = ra₁ = - 0.7071 (4)           = - 2.8284

a₃ = ra₂ = - 0.7071 (-2.8284) = + 2.0000

a₄ = ra₃ = - 0.7071 (2.0000)  =  - 1.4142

a₅ = ra₄ = - 0.7071 (-1.4142) = + 1.0000

 

BTW, if you do a little math on that formula for a_k,  you get another way of expressing it:

a_k = a₁ r^(k-1) for k = 2, 3, ...   Thus a5 = (+4) (-0.7071)⁴ = (+4) (+0.2500) = + 1.0000 as before.

Because the constant r keeps getting multiplied, someone named this series geometric.