Final answer:
To find the first term and the common difference of an arithmetic sequence, use the given information to set up and solve a system of equations.
Step-by-step explanation:
To find the first term and the common difference of an arithmetic sequence, we can use the given information. From the problem, we know that the fifth term of the sequence is 6, and the sum of the first 12 terms is 45.
Let's use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Substituting the values we know, we have:
6 = a1 + 4d - (1)
Next, let's use the formula for the sum of the first n terms of an arithmetic sequence:
Sn = n/2 * (a1 + an)
Substituting the values we know, we have:
45 = 12/2 * (a1 + a12)
By solving these two equations simultaneously, we can find the values of a1 and d.