`10, 5, 0, -5, -10` Find a formula for a_n for the arithmetic sequence.

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The given first few terms of the arithmetic sequence are:

`{10, 5, 0, -5, -10...}`

Take note that the nth term of an arithmetic series is `a_n =a_1 + (n-1)d` . Since the first term a_1 is known already, let's solve for the value of d. d is the common...

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The given first few terms of the arithmetic sequence are:

`{10, 5, 0, -5, -10...}`

Take note that the nth term of an arithmetic series is `a_n =a_1 + (n-1)d` . Since the first term a_1 is known already, let's solve for the value of d. d is the common difference of the consecutive terms of an arithmetic sequence.

`d=a_2-a_1 = 5-10=-5`

`d=a_3-a_2 = 0 - 5 = -5`

`d=a_4-a_3=-5-0 = -5`

`d=a_5-a_4 = -10 - (-5)=-5`

So the common difference is d = -5.

Then, plug-in `a_1=10` and `d=-5` to the formula of nth term of arithmetic sequence.

`a_n =a_1 + (n-1)d`

`a_n=10 + (n-1)(-5)`

`a_n = 10 -5n + 5`

`a_n=15-5n`

Therefore, the nth term of the given arithmetic sequence is `a_n=15 - 5n` .

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