Final answer:
To find the explicit formula for the arithmetic sequence, substitute the given values into the formula and solve for the common difference. Then, substitute the common difference back into the formula to get the explicit formula.
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To find an explicit formula for this arithmetic sequence, we can use the formula:
a(n) = a(1) + (n - 1)d
where a(n) is the n-th term of the sequence, a(1) is the first term, n is the term number, and d is the common difference. Given that a(1) = -4 and a(6) = 46, we can substitute these values into the formula:
a(6) = -4 + (6 - 1)d = -4 + 5d = 46
Solving for d, we get d = (46 + 4) / 5 = 10. Substituting this value back into the formula, we have:
a(n) = -4 + (n - 1)10 = -4 + 10n - 10 = 10n - 14
Therefore, the explicit formula for this arithmetic sequence is a(n) = 10n - 14.