# 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

 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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