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Using Algebra Sequences Practice Questions (page 2)

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Updated on Oct 3, 2011

Practice 2

1. The formula tn = t1(rn – 1) gives us the value of any term in a geometric sequence. The first term, t1, 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:
t7 = 4(3x7 – 1)
t7 = 4(3x6)
t7 = 4(729)
t7 = 2,916
The seventh term in the sequence is 2,916.
2. The formula tn = t1(rn – 1) gives us the value of any term in a geometric sequence. The first term, t1, 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:
t6 = (x – 1)(46 – 1)
t6 = (x – 1)(45)
t6 = (x – 1)(1,024)
t6 = 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 tn = t1(rn – 1) gives us the value of any term in a geometric sequence. The first term, t1, 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:  
t8 = (15x + 8)
t8 = (15x + 8)
t8 = (15x + 8)
t8 =
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 tn = t1(rn – 1) gives us the value of any term in a geometric sequence. The first term, t1, 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:
t5 = (–65– 1)
t5 = (–64)
t5 = (1,296)
t5 = –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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