Question

Which of the following is not a geometric sequence?

Answer 1

The sequence -7 , -5.8 , -4.6 , -3.4 , -2.2 is not a geometric sequence

Step-by-step explanation:

In the geometric sequence, there is a constant ratio between each two consecutive terms

To prove that a sequence is geometric

• Find the ratio between each two consecutive terms $\frac{a_{2}}{a_{1}}$ , $\frac{a_{3}}{a_{2}}$ , $\frac{a_{4}}{a_{3}}$ , .....
• If all the answers give the same ratio, then the sequence is geometric, if not then the sequence is not geometric

The first sequence is 2.8 , 6.72 , 16.128 , 38.7072

∵ $a_{1}$ = 2.8

∵ $a_{2}$ = 6.72

∴ $r=\frac{6.72}{2.8}=2.4$

∵ $a_{2}$ = 6.72

∵ $a_{3}$ = 16.128

∴ $r=\frac{16.128}{6.72}=2.4$

∵ $a_{3}$ = 16.128

∵ $a_{4}$ = 38.7072

∴ $r=\frac{38.7072}{16.128}=2.4$

∵ All the ratios above are equal 2.4

∴ The sequence is a geometric sequence

The second sequence is -7, -5.8 , -4.6 , -3.4 , -2.2

∵ $a_{1}$ = -7

∵ $a_{2}$ = -5.8

∴ $r=\frac{-5.8}{-7}=\frac{29}{35}$

∵ $a_{2}$ = -5.8

∵ $a_{3}$ = -4.6

∴ $r=\frac{-4.6}{-5.8}=\frac{23}{29}$

∵ The first two ratios are not equal

∴ The sequence is not a geometric sequence

The third sequence is 1 , -3 , 9 , -27 , 81

∵ $a_{1}$ = 1

∵ $a_{2}$ = -3

∴ $r=\frac{-3}{1}=-3$

∵ $a_{2}$ = -3

∵ $a_{3}$ = 9

∴ $r=\frac{9}{-3}=-3$

∵ $a_{3}$ = 9

∵ $a_{4}$ = -27

∴ $r=\frac{-27}{9}=-3$

∵ $a_{4}$ = -27

∵ $a_{5}$ = 81

∴ $r=\frac{81}{-27}=-3$

∵ All the ratios above are equal -3

∴ The sequence is a geometric sequence

The sequence -7 , -5.8 , -4.6 , -3.4 , -2.2 is not a geometric sequence

Learn more:

You can learn more about the geometric sequence in brainly.com/question/1522572

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Answer 2

Answer b ok ok ok

ok ok ok