Answer: k = 3
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Explanation:
- A = first term = k+2
- B = second term = 4k-6
- C = third term = 3k-2
To go from the first term to the second term, we add on some common difference d.
So,
B = A+d
B = (k+2)+d
4k-6 = k+2+d
4k-6-k-2 = d
d = 3k-8
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Similarly, to go from the second term to the third term, we also add on d
C = B+d
C = (4k-6)+d
C = (4k-6)+(3k-8)
C = 7k-14
3k-2 = 7k-14
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Let's solve for k
3k-2 = 7k-14
-2+14 = 7k-3k
12 = 4k
4k = 12
k = 12/4
k = 3 is the final answer
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If k = 3, then we have these three terms:
- A = k+2 = 3+2 = 5
- B = 4k-6 = 4(3)-6 = 6
- C = 3k-2 = 3(3)-2 = 7
The arithmetic progression (AP) is 5, 6, 7. The common difference is d = 1.
Note how d = 3k-8 = 3(3)-8 = 1
