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

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

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

The total would be 40.53