Question 629829
What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374? 

{{{S[n] = (n/2)(a[1] + a[n])}}}

{{{S[43] = (43/2)(a[1] + a[43])}}}

{{{9374 = (43/2)(-13 + a[43])}}}

{{{436 = -13 + a[43]}}}

{{{a[43] = 449}}}

{{{a[n] = a[1] + (n-1)d}}}

{{{a[43] = -13 + (43-1)d}}}

{{{449 = -13 + 42d}}}

{{{highlight(d = 11)}}}

The common difference is 11

What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10? 

{{{a[n] = a[1] + (n-1)d}}}
{{{a[12] = a[1] + (12-1)(-10)}}}
{{{13 = a[1] - 110}}}
{{{a[1] = 123}}}

{{{S[n] = (n/2)(a[1] + a[n])}}}
{{{S[12] = (12/2)(123 + 13)}}}
{{{s[12] = highlight(816)}}}

Provide an example of an arithmetic series which totals zero. Using complete sentences, explain how you created the example
{{{highlight((-8) + (-6) + (-4) + (-2) + 0 + 2 + 4 + 6 + 8)}}} is an example of an arithmetic series which totals zero. 
The term of the arithmetic sequence should include zero and multiples of a common difference. The first and last term should be numerically equal but opposite in sign.