Final answer:
Using the assumption of a linear relationship, t12 would be calculated as 20, which is not listed in the provided options. Since the calculated value is not an option, the relationship might be non-linear, or there might be an error in the question or options.
Step-by-step explanation:
To find t12 when given t8 = 12 and t20 = 36, we can assume that there is a linear relationship between the term number and the value of the term. This means that as the term number increases, the value of each term increases at a constant rate. The difference between term 20 and term 8 is 12 terms (20 - 8), and the corresponding difference in their values is 36 - 12 = 24. This means that each term increases by 24 / 12 = 2 with each step.
Since t8 is 12, and we need to find t12, we have 4 steps between them (12 - 8). Multiplying these 4 steps by an increase of 2 per step gives us 4 * 2 = 8. Adding this to the value of t8: 12 + 8, we get t12 = 20. However, this value does not appear in the options given. This could mean the relationship is not precisely linear or there may have been a mistake in the question or the options provided. Since none of the options includes 20, which is the answer according to linear progression, we might need more information to provide an accurate answer.