The question is incomplete as it doesn't specify the last term of the arithmetic progression. To find the 12th term from the end, we need the last term. Several sources provide solutions for similar problems, assuming a final term of -100. Let's use that assumption to illustrate the method and then address the issue of an incomplete question.
Solution with Assumed Last Term (-100)
Many resources address a similar problem using the arithmetic progression -2, -4, -6,..., -100. This arithmetic progression shares the same common difference (d = -2) as the provided progression 2, 4, 6..., but starts at a different point. Let's adapt their solution method.
The 12th term from the end of an arithmetic progression can be calculated using the formula:
l - (n - 1)d
Where:
- l is the last term
- n is the number of terms from the end (in this case, 12)
- d is the common difference
Using the provided references and adapting it to the assumed progression of -2, -4, -6,...-100:
- l = -100
- n = 12
- d = -2
The 12th term from the end is: -100 - (12 - 1)(-2) = -100 + 22 = -78
Therefore, if the arithmetic progression were -2, -4, -6,...,-100, the 12th term from the end would be -78. Multiple sources confirm this (Byjus, Cuemath, Toppr).
Addressing the Incomplete Question
The original question lacks a crucial piece of information: the final term of the arithmetic progression. Without knowing the last term, we cannot definitively determine the 12th term from the end. The example calculations above demonstrate the method if the progression were extended to include a final term of -100, but this is an assumption based on similar problems available in online resources.
