Part A
Answer: x = 20
--------------------------------
Explanation:
AP = arithmetic progression, which is another way of saying arithmetic sequence.
Let d = common difference
- first term = 10
- second term = first+d = 10+d = x
- third term = second+d = x+d = 30
Apply substitution like so
x+d = 30
10+d+d = 30 ... replaced x with 10+d
10+2d = 30
2d = 30-10
2d = 20
d = 20/2
d = 10 is the common difference
Therefore,
x = 10+d = 10+10 = 20
The AP {10,x,30} updates to {10,20,30}. We see the gap between terms is 10 units. All AP's have the same gap width between adjacent terms.
=============================================================
Part B
Answers: x = 10 and y = 14
--------------------------------
Explanation:
We use the same ideas mentioned back in part A.
d = common difference = unknown for now
- first term = 6
- second term = first+d = 6+d = x
- third term = second+d = x+d = (6+d)+d = 6+2d = y
- fourth term = third+d = y+d = (6+2d)+d = 6+3d = 18
Hopefully you can see how each term builds up to form the next one. We'll solve that last equation like so
6+3d = 18
3d = 18-6
3d = 12
d = 12/3
d = 4
So we then can say:
- x = 6+d = 6+4 = 10
- y = 6+2d = 6+2(4) = 6+8 = 14
The arithmetic sequence {6,x,y,18} updates to {6,10,14,18}. There's a gap of 4 between each adjacent term.
