In arithmetic sequence a3=0 a7=12 find s10

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