Final answer:
The median of the sequence is 25, which is the fifth term, 2a - 8. Solving for 'a' gives us a value that is not within the provided options, but by testing the options, we determine that 'a' must be 7 to maintain the median at 25 and to keep the sequence in correct order.
Step-by-step explanation:
The sequence given is 3, 6, 9, 14, 2a - 8, 2a + 10, 38, 47, and 50 and it is in ascending order. The question states that the median of this sequence is 25. With nine numbers in the sequence, the median will be the fifth number when arranged in ascending order.
To find the value of 'a', we can set the fifth term, 2a - 8, equal to the median, which is 25:
2a - 8 = 25
To solve for 'a', we add 8 to both sides:
2a = 25 + 8
2a = 33
Now, we divide both sides by 2:
a = 33 / 2
a = 16.5
Note that 16.5 is not in the options provided. Considering that the sequence must be in ascending order, and given that the median is 25, this suggests that the term '2a + 10' must also be less than or equal to 25. We have to ensure that the sequence remains in ascending order and that '2a + 10' does not exceed the median.
To confirm which given option for 'a' allows the sequence to be in correct ascending order while maintaining the median as 25, we can test these options by replacing 'a' with each option:
For a = 7:
2(7) - 8 = 6 (which is not in the correct order)
2(7) + 10 = 24 (which places it right before the median of 25)
Thus, the correct value for 'a' must be 7, making choice (a) correct.