arithmetic series

A formula for the sum of the terms of a finite arithmetic sequence is:  Sum  =  n(t₁ + t_n)/2

where  n = number of terms      t₁ = first term      t_n = n^th term (last term)

For this problem,  n = 18      t₁ = -9     t₁₈ = unknown.

 

So, we need to find t₁₈.

A formula for the n^th term is:  t_n  =  t₁ + (n - 1)d

where  d = common difference.

For this problem,  d = -5      n = 18.

 t_n  =  t₁ + (n - 1)d     --->      t_n  =  -9 + (18 - 1)(-5)  =  -94

 

Sum  =  n(t₁ + t_n)/2     --->     Sum  =  18(-9 + -94)/2     --->     Sum  =  -927