Final answer:
In an arithmetic sequence, the value of a_1 can be found by using the formula a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference. By using the given information and solving for n, we find that a_1 is equal to 5.
Step-by-step explanation:
The given sequence is 5, 12, 19, ... , 68. To find the value of a_1, we need to determine the common difference, d.
The common difference is obtained by subtracting any two consecutive terms in the sequence.
Let's subtract 12 from 5: 12 - 5 = 7. Therefore, d = 7.
The formula to find the nth term of an arithmetic sequence is: a_n = a_1 + (n - 1) * d.
We can now substitute the given values to find a_n.
Let's use the last term, 68, to find n: 68 = a_1 + (n - 1) * 7. Since we know a_1 = 5 and d = 7, we can solve for n.
68 = 5 + (n - 1) * 7.
Simplifying the equation gives us: 68 = 5 + 7n - 7. Solving for n, we get n = 10.
Therefore, the value of a_1 is 5.