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College Algebra - Geometric Sequence

by Bart
(Los Fresnos, TX)











































Find common ratio and write out the first four terms of the geometric sequence {bn}={(5/2)^n}

Comments for College Algebra - Geometric Sequence

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Apr 25, 2011
Geometric Sequence, Terms, Common Ratio
by: Staff


The question:

Find common ratio and write out the first four terms of the geometric sequence {bn} = {(5/2)^n}


The answer:


A geometric sequence has the (general) form:

b_n = b_1 * (r)^(n - 1)


b_n = b with a subscript of n (this is the nth term in the sequence)
b_1 = a with a subscript of 1 (this is the 1st term in the sequence)

n = number of terms

r = the common ratio


The first four terms in the geometric sequence:


b_n = (5/2)^n


If n = 1, the first term is

b_1 = (5/2)^1

b_1 = 5/2


If n = 2, the second term is

b_2 = (5/2)^2

b_2 = 5^(2)/2^(2)

b_2 = 25/4



If n = 3, the third term is

b_3 = (5/2)^3

b_3 = 5^(3)/2^(3)

b_3 = 125/8



If n = 4, the fourth term is

b_4 = (5/2)^4

b_4 = 5^(4)/2^(4)

b_4 = 625/16



b_n = 5/2, 25/4, 125/8, 625/16, . . .

r, the common ratio, can be calculated as follows:
r_n = b_n/b_n-1
(n must be greater than 1)

r_n = r with a subscript of n (this is the common ratio)

b_n = a with a subscript of n (this is the nth term in the sequence)

b_n-1 = a with a subscript of n-1 (this is the n-1 term in the sequence)


using the 2nd and 3rd terms in the sequence to calculate the common ratio

b_2 = 25/4

b_3 = 125/8

r_n = b_n/b_n-1

r_n = b_3/b_2

r_n = (125/8)/( 25/4)

r_n = (125/8)*(4/25)

r_n = (125/25)*(4/8)

r_n = 5*(1/2)

r_n = (5*1)/(2)

r_n = 5/2

r, the common ratio = 5/2 = 2.5

the final answer is:

the first four terms of the geometric series are:

b_n = 5/2, 25/4, 125/8, 625/16, . . .

the common ratio: = 5/2 = 2.5



the standard form of the geometric sequence is:

b_n = b_1 * (r)^(n - 1)

b_n = (5/2) * (5/2)^(n - 1)



Thanks for writing.


Staff
www.solving-math-problems.com


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