By LearningExpress Editors
Updated on Oct 3, 2011
Practice 2
1.  The formula t_{n} = t_{1}(r^{n – 1}) gives us the value of any term in a geometric sequence. The first term, t_{1,} is 4. 
The ratio, r, can be found by dividing any pair of consecutive terms: 12 ÷ 4 = 3x, so r = 3x. Because we are looking for the seventh term, n = 7:  
t_{7} = 4(3x^{7 – 1})  
t_{7} = 4(3x^{6})  
t_{7} = 4(729)  
t_{7} = 2,916  
The seventh term in the sequence is 2,916.  
2.  The formula t_{n} = t_{1}(r^{n – 1}) gives us the value of any term in a geometric sequence. The first term, t_{1,} is x – 1. 
The ratio, r, can be found by dividing any pair of consecutive terms. Divide the third term by the second term, because this will cause the variable x to be canceled: 8x ÷ 2x = 4, so r = 4. Because we are looking for the sixth term, n = 6:  
t_{6} = (x – 1)(4^{6 – 1})  
t_{6} = (x – 1)(4^{5})  
t_{6} = (x – 1)(1,024)  
t_{6} = 1,024x – 1,024  
The ratio between any two consecutive terms in the sequence is 4. That means that the second term, 2x, divided by the first term, x – 1, is equal to 4. Solve this equation for x:  
= 4  
(x – 1) = (x – 1)4  
2x = 4x – 4  
–2x = –4  
x = 2  
The value of x in this sequence is 2, which means that the sixth term, 1,024x – 1,024, is equal to 1,024(2) – 1,024 = 2,048 – 1,024 = 1,024.  
3.  The formula t_{n} = t_{1}(r^{n – 1}) gives us the value of any term in a geometric sequence. The first term, t_{1,} is 15x + 8. 
The ratio, r, can be found by dividing any pair of consecutive terms. Divide the third term by the second term, because this will cause the variable x to be canceled: 4x ÷ 8x = so r = Because we are looking for the eighth term, n = 8:  
t_{8} = (15x + 8)  
t_{8} = (15x + 8)  
t_{8} = (15x + 8)  
t_{8} =  
The ratio between any two consecutive terms in the sequence is That means that the second term, 8x, divided by the first term, 15x + 8, is equal to Solve this equation for x:  
16x = 15x + 8  
x = 8  
The value of x in this sequence is 8, which means that the eighth term, , is equal to = 1.  
4.  The formula t_{n} = t_{1}(r^{n – 1}) gives us the value of any term in a geometric sequence. The first term, t_{1,} is . 
The ratio, r, can be found by dividing any pair of consecutive terms. Divide the fourth term by the third term, because this will cause the variable x to be canceled: 12x ÷ –2x = –6, so r = –6. Because we are looking for the fifth term, n = 5:  
t_{5} = (–6^{5– 1})  
t_{5} = (–6^{4})  
t_{5} = (1,296)  
t_{5} = –72x  
The ratio between any two consecutive terms in the sequence is –6. That means that the third term, –2x, divided by the second term, x – 2, is equal to –6. Solve this equation for x:  
= –6  
–2x = –6x + 12  
4x = 12  
x = 3  
The value of x in this sequence is 3, which means that the fifth term, –72x, is equal to –72(3) = –216. 
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From Algebra in 15 Minutues A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.
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