Answer:
1.4, 0.28, 0.056
Step-by-step explanation:
Each number is divided by 5
(875/5=175 175/5=35)
Answer:
The next three terms of the geometric sequence are 875, 175, 35, 7 is 1.4, 2.8, and 0.56.
Solution:
Given Geometric sequence is 875, 175, 35, 7.
We need to find the next three sequence.
A geometric sequence is one where any value in the sequence can be determined using the formula:
[tex]\boldsymbol{a}_{\mathbf{n}=\mathbf{a}_{1}(\mathbf{r})^{n-1}}[/tex]
Where
n is the nth term in the sequence, [tex]a_{1}[/tex] is the first term (in this case, 875) and "r" is the rate of change between them.
To find r, you simply divide the second term by the first:
[tex]\frac{175}{875} = 0.2[/tex]
Inserting [tex]a_{1}[/tex] = 875 and r=0.2 into the formula above, you have the equation for the sequence:
[tex]a_{5}=875 \times(0.2)^{n-1}[/tex]
To find 5th sequence:
[tex]a_{5=875 \times(0.2)^{5-1}}=875 \times(0.2)^{4}=875 \times 0.0016=1.4[/tex]
To Find 6th Sequence:
[tex]a_{5=875 \times(0.2)^{6-1}}=875 \times(0.2)^{5}=875 \times 0.0032=0.28[/tex]
To Find 7th Sequence:
[tex]a_{5}=875 \times(0.2)^{7-1}=875 \times(0.2)^{6}=875 \times 0.000064=0.056[/tex]
Hence the next three terms of the geometric sequence are 875, 175, 35, 7, 1.4, 0.28, and 0.056.
