In
order to solve for a nth term in an arithmetic sequence, we use the formula
written as:
an = a1 + (n-1)d
where an is the nth term, a1 is the first value
in the sequence, n is the term position and d is the common difference.
First, we need to calculate for d from the given
values above.
a3 = 0 and a7 = 12
an = a1 + (n-1)d
0 = a1 + (3-1)d
an = a1 + (n-1)d
12 = a1 + (7-1)d
Solving simultaneously we get,
a1 = -6
d = 3
The sum would be calculated as follows:
S = (10/2) × (2(-6) + (10-1)3)
S = 75
