Answer:
The sequence is geometric.
Step-by-step explanation:
If the sequence is arithmetic common difference will be same, if the sequence is arithmetic common ratio will be same.
Here the sequence is 4, 40, 400, 4000, …
Difference between terms
40 -4 = 36
400 - 40 = 360
They are not same , so the sequence is not arithmetic.
Ratio between terms
40/4 = 10
400/40 = 10
4000/400 = 10
They are same , so the sequence is geometric.
Now we need to find recursive formula for the sequence.
Recursive formula for GP
13 should be b and
14 is a because geometric mean to have a common ratio
This is the concept of algebra, suppose that the number of cats is x;
number of cats will be x-20
number of rabbits will be 3/2x
thus the total number of animals will be:
x+(x-20)+3/2x=350
7/2x=350+20
7/2x=370
x=370*2/7
x=105.7=106
therefore we conclude that there we 106 cats in the shelter
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