Answer :
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 [tex]\frac{a_{2}}{a_{1}}[/tex] , [tex]\frac{a_{3}}{a_{2}}[/tex] , [tex]\frac{a_{4}}{a_{3}}[/tex] , .....
- 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
∵ [tex]a_{1}[/tex] = 2.8
∵ [tex]a_{2}[/tex] = 6.72
∴ [tex]r=\frac{6.72}{2.8}=2.4[/tex]
∵ [tex]a_{2}[/tex] = 6.72
∵ [tex]a_{3}[/tex] = 16.128
∴ [tex]r=\frac{16.128}{6.72}=2.4[/tex]
∵ [tex]a_{3}[/tex] = 16.128
∵ [tex]a_{4}[/tex] = 38.7072
∴ [tex]r=\frac{38.7072}{16.128}=2.4[/tex]
∵ 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
∵ [tex]a_{1}[/tex] = -7
∵ [tex]a_{2}[/tex] = -5.8
∴ [tex]r=\frac{-5.8}{-7}=\frac{29}{35}[/tex]
∵ [tex]a_{2}[/tex] = -5.8
∵ [tex]a_{3}[/tex] = -4.6
∴ [tex]r=\frac{-4.6}{-5.8}=\frac{23}{29}[/tex]
∵ The first two ratios are not equal
∴ The sequence is not a geometric sequence
The third sequence is 1 , -3 , 9 , -27 , 81
∵ [tex]a_{1}[/tex] = 1
∵ [tex]a_{2}[/tex] = -3
∴ [tex]r=\frac{-3}{1}=-3[/tex]
∵ [tex]a_{2}[/tex] = -3
∵ [tex]a_{3}[/tex] = 9
∴ [tex]r=\frac{9}{-3}=-3[/tex]
∵ [tex]a_{3}[/tex] = 9
∵ [tex]a_{4}[/tex] = -27
∴ [tex]r=\frac{-27}{9}=-3[/tex]
∵ [tex]a_{4}[/tex] = -27
∵ [tex]a_{5}[/tex] = 81
∴ [tex]r=\frac{81}{-27}=-3[/tex]
∵ 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
#LearnwithBrainly