Question

Pls help me out here which places do they go

Answer 1

Answer:

1,2,4,8 is geometric

1,3,5,7 is arithmetic

-3,-6,-9,-12 geometric

50,100,150,200 geometric

250,50,10,2 arithmetic

2,-6,18,-54  arithmetic  

Answer 2

Answers:

Geometric:

• 1, 2, 4, 8, ...
• 250, 50, 10, 2, ...
• 2, -6, 18, -54, ...

Arithmetic:

• -3, -6, -9, -12, ...
• 50, 100, 150, 200, ...
• 1, 3, 5, 7, ...

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Explanation:

A geometric sequence is one where we generate terms by multiplying each term by the same number to get the next number.

In the case of {1,2,4,8,...} we multiply each term by 2.

• first term = 1
• second term = 2*(first term) = 2*1 = 2
• third term = 2*(second term) = 2*2 = 4
• fourth term = 2*(third term) = 2*4 = 8

And so on. We say the common ratio is 2.

For the geometric sequence {250, 50, 10, 2, ...} the common ratio is 1/5 since 250*1/5 = 50 and 50*1/5 = 10, etc.

For the geometric sequence {2, -6, 18, -54, ...} we are multiplying each term by -3.

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Arithmetic sequences are similar to geometric ones. Instead of multiplying, we add on the same thing each time to get new terms.

The sequence {-3, -6, -9, -12, ...} is arithmetic because we are adding on -3 each time

• first term = -3
• second term = (first term) + (-3) = (-3)+(-3) = -6
• third term = (second term) + (-3) = (-6)+(-3) = -9
• fourth term = (third term) + (-3) = (-9)+(-3) = -12

This process goes on for as long as you want. We say the common difference is -3

For the arithmetic sequence {50, 100, 150, 200, ...} the common difference is 50 because we are adding 50 on each time to get a new term.

The arithmetic sequence {1, 3, 5, 7, ...} has the common difference 2.