Match the like terms 1.) -12x^2 2.) 11 3.) 8xy^3 4.) -3y^2 5.) 6xy

Mathematics

1 answer:

frutty [35]3 years ago

4 0

Like terms have the same variable part. That means the variables and exponents must be the same.

1.) -12x^2 a.) 5x^2

2.) 11 e.) -6

3.) 8xy^3 b.) 4xy^3

4.) -3y^2 c.) 15y^2

5.) 6xy d.) 14xy

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PLEASE HELP!!!!!!!!!!!!!!!

vampirchik [111]

Problem 1)

The notation you wrote down is a bit odd. There seems to be a typo. Please double check.

Assuming you meant to write

$a_{n} = 3 a_{n-1}$

then the answer is choice D) 2, 6, 18, 54, 162, ...

-------

Why is this? Because each term is found by multiplying the previous term by 3

first term = 2

second term = (first term)*3 = 2*3 = 6

third term = (second term)*3 = 6*3 = 18

fourth term = (third term)*3 = 18*3 = 54

fifth term = (fourth term)*3 = 54*3 = 162

this pattern continues forever

Extra information: The closed form equation is $a_{n} = 2(3)^{n-1}$ where 2 is the first term, 3 is the common ratio, and n is a positive integer.

some more info: notice picking any term in sequence {2,6,18,54,162,...} and dividing it over its previous term leads to 3

6/2 = 3

18/6 = 3

54/18 = 3

162/54 = 3

None of the other sequences listed have this property of the adjacent terms dividing to a constant ratio. So none of the other sequences are geometric.

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Problem 2)

The first term is $t_{1} = 2$ (ie, the first term is 2)