Final answer:
To find the value of the first term, we need to use the formula for the nth term of an arithmetic sequence and solve for the first term. By substituting the given values for the ninth and fourth terms and solving the resulting equations, we can find the value of the first term.
Step-by-step explanation:
To find the value of the first term, we need to use the formula for the nth term of an arithmetic sequence. The formula is given by:
nth_term = first_term + (n-1) * common_difference
Using the given information, we can substitute the values and solve for the first term:
123 = first_term + 8 * common_difference
321 = first_term + 3 * common_difference
By subtracting the two equations, we can eliminate the first term and solve for the common difference:
-198 = 5 * common_difference
common_difference = -198/5
Substituting the common difference back into one of the previous equations, we can solve for the first term:
123 = first_term + 8 * (-198/5)
first_term = 123 - 8 * (-198/5)
Simplifying the expression gives the value of the first term:
first_term ≈ 246.6