```Question 149402
Lets assume this sequence is an arithmetic sequence. The general form of the arithmetic sequence is

{{{a[n]=d*n+a[1]}}} where {{{a[n]}}} is the nth term, d is the difference, and {{{a[1]}}} is the first term

So lets find the difference between 2 terms (i.e. the difference between two terms)

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To find the difference, simply pick any term and subtract the previous term from that selected term

{{{19-21=-2}}} Select the 2nd term (which is 19) and subtract the 1st term (which is 21) from it.

So we get a difference of {{{-2}}}

Lets pick another pair of terms to verify:

{{{17-19=-2}}} Select the 3rd term (which is 17) and subtract the 2nd term (which is 19) from it.

And again, we get a difference of {{{-2}}}

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Lets pick another pair of terms to verify:

{{{15-17=-2}}} Select the 4th term (which is 15) and subtract the 3rd term (which is 17) from it.

And again, we get a difference of {{{-2}}}

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Since we've tested every consecutive pair of terms, we've verified that the sequence has a constant difference of  {{{-2}}}. This means the sequence is arithmetic

Since the difference is {{{d=-2}}} and the first term is {{{a[1]=21}}}, this means the arithmetic sequence is

{{{a[n]=-2n+21}}}  where {{{n}}} starts at {{{n=0}}}

Check:

Notice if we plug in {{{n=0}}} we get

{{{a[0]=-2(0)+21}}} plug in {{{n=0}}}

{{{a[0]=0+21}}} Multiply

which is our first term

Notice if we plug in {{{n=1}}} we get

{{{a[1]=-2(1)+21}}} plug in {{{n=1}}}

{{{a[1]=-2+21}}} Multiply

which is our second term

Notice if we plug in {{{n=2}}} we get

{{{a[2]=-2(2)+21}}} plug in {{{n=2}}}

{{{a[2]=-4+21}}} Multiply

which is our third term

Notice if we plug in {{{n=3}}} we get

{{{a[3]=-2(3)+21}}} plug in {{{n=3}}}

{{{a[3]=-6+21}}} Multiply

which is our fourth term

Since each term corresponds to the terms of the given list, this verifies our sequence.

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