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which of these is a formula that can be used to determine the nth term of the arithmetic sequence 15,27,39,51,....?

which of these is a formula that can be used to determine the nth term of the arithmetic-example-1
User Hgminh
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a_n=\text{ }12n+3\text{ (}optionB)Step-by-step explanation:

For an arithmetric progression, we need to find the common difference in the sequence

common difference = d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term

2nd term - 1st term = 27 -15 = 12

3rd term - 2nd term = 39-27 = 12

The result are the same.

Hence, d = 12

The first trm = 15

The formula for arithmetric sequence:

The nth term = 1st term + d(n - 1)

Replacing with the values we got above:

The nth term = 15 + 12(n - 1)

Since none of the options have the above, we would expand the parenthesis.

The nth term = 15 + 12×n - 12×1

The nth term = 15 + 12n - 12

= 15 -12 + 12n

The nth term = 3 + 12n = 12n + 3

From the options:

The nth term = 12n + 3 (option B)


a_n=\text{ }12n+3\text{ (}optionB)

User Sakinah
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