Question

In arithmetic sequence a3=0 a7=12 find s10

Answer 1

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