Question

complete the resursive of the geometric sequence 10,6,3.6,2.16

Answer 1

Answer:

a(n) = (3/5)a(n-1), where a(1) = 10 and n is 2 or greater.

Step-by-step explanation:

First determine the common factor.  Note that mult. the first term (10) by 3/5 results in the given second term (6); the third term is 3/5 of the second term (6), resulting in 18/5 (equivalent to 36/10 or 3.6/1, or just 3.6.  And so on.

Thus, a(n) = (3/5)a(n-1).  We can demo that this "works" for the fourth term:

the third term is 3.6, which, if mult. by (3/5), produces 2.16, as expected.

Thus, the recursive formula for this geometric sequence is a(n) = (3/5)a(n-1).

This is good only for a(1) = 10 and n = {2, 3, .... }

Answer 2

The recursive of geometric sequence 10,6,3.6,2.16 is  

$a_{n} =0.6\;a_{n-1}$

We have the following geometric sequence - 10,6,3.6,2.16.

We have to find the recursive of this geometric sequence.

What is the formula to find the recursive of a Geometric sequence?

The formula to find the recursive of geometric sequence is -

$a_{n} =r\;a_{n-1}$        $for\;n\geq\;2$

We can use the above formula to find the recursive of the geometric sequence as follows -

Find the value of common ratio (r)  :

$r = \frac{a_{2} }{a_{1} } \\r=\frac{6}{10}\\r=0.6$

Substituting the value of in the formula for finding the recursive, we get -

$a_{n} =0.6\;a_{n-1}$

Hence, the recursive of geometric sequence 10,6,3.6,2.16 is - $a_{n} =0.6\;a_{n-1}$

To solve more questions on finding the recursive of geometric sequence, visit the following link -

brainly.com/question/24506976

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