Quandaries and Queries
  

 

Hi,
My name is Lesa and my daughter who is a senior has a tough question that I have no clue on how to solve. Can you help us?
1. Find a formula for the geometric sequence: (√3 - √2), (4 - √6), (6√3 - 2√2), …

2. Find the sum of the first five terms
 

 

Hi Lesa,

A geometric sequence has the form

a, ar, ar2, ar3, ...

a is the first term and r is the common ratio. If your sequence is a geometric sequence then

a = √3 - √2

and

(√3 - √2) r = (4 - √6).

Thus

r = (4 - √6)/(√3 - √2) = (4 - √6)/(√3 - √2)  (√3 + √2)/(√3 + √2)

= (4√3 + 4√2 - √18 - √12)/3 - 2 = 2√3 + √2

Thus

r = 2√3 + √2

Now check that the sequence is a geometric series by verifying that

(4 - √6) (2√3 + √2) = (6√3 - 2√2)

Penny

 

  
 

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