A problem involving arithmetic progressions

Question

A diagram shows three cylinders such that the volume for each is arranged according to arithmetic progression. The sum of the volume for the 1st and 3rd cylinder is 24 cm^3 and the volume of the fifth cylinder is 36 cm^3.

(which is just x,y,z,a,b in order where with given info becomes x,y,z,a,36 and x+z=24.)

(a) Find the volume of the 1st cylinder.

(B) Calculate the sum of volume for the first 9 cylinders.

Answer 1

Hints:

• Call the first term of the progression $a$, the second $a+d$, the third $a+2d$ and so on.
• You have two simultaneous equations involving $24$ and $36$.
• Solve them for $a$ and $d$.
• Answer the two questions