Answer:
Step-by-step explanation:
First I want to set up some variables.
S = sum
n = final term
ax = xth term, so a1 is the first term and an is the last one
d = common difference.
There are two formulas to find the sum, if you don't get how they were gotten I'd be happy to explain.
S = (n/2)(a1+an) = (n/2)(2a1+(n-1)d)
So, to find n we use the first one.
S = (n/2)(a1+an)
123 = (n/2)(8+33)
123 = (n/2)41
3 = n/2
6 = n
Now we can find d with the other one
S = (n/2)(2a1+(n-1)d)
123 = (6/2)(2*8+(6-1)d)
123 = 3(16+5d)
41 = 16+5d
25 = 5d
5 = d
so there are six terms and the common difference is 5.
