Question

The third term of an arithmetic sequence is -12 and the 7th term is 8. What is the sum of the first 10 terms?

Answer 1

3rd term=-12
7th term= 8
First find the first term and the common difference;

From the general equation of Arithmetic sequence;
3rd term;
-12=a+(3-1)d
-12=a+2d
7th term;
8=a+6d

Solving the simultaneous equation;
8  =a+6d
-12=a+2d       on subtracting;
------------
20=4d
d=5

Finding value of a using equation 1 above;
8=a+6d
8=a+30
a=-24
Sum of first 10 terms;
s(10)=n/2(2a+(n-1)d)
s(10)=10/2(-48+9*5)
s(10)=5(-3)
s(10)=-15