Answer: Let's call the first term of the arithmetic sequence "a", and the common difference between the terms "d".
Then, we know that the sum of the first 8 terms is 88, so we can write:
a + (a + d) + (a + 2d) + ... + (a + 7d) = 88
Using the formula for the sum of an arithmetic sequence, we can simplify this to:
8a + 28d = 88
We also know that the product of the 1st and 8th terms is 120, so we can write:
a(a + 7d) = 120
Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable.
Solving the first equation for d:
d = (88 - 8a)/28
Substituting into the second equation:
a(a + 7[(88-8a)/28]) = 120
Multiplying both sides by 28 to eliminate the fraction:
28a^2 + 154a - 960 = 0
We can factor this quadratic equation as:
(2a - 15)(14a + 64) = 0
So either 2a - 15 = 0 or 14a + 64 = 0. Solving for "a" in each case, we get:
a = 15/2 or a = -64/14
Since we're looking for the first term of the sequence, which must be positive, we can discard the negative value and conclude that the first term is:
a = 15/2
Therefore, the first term of the arithmetic sequence is 7.5.
Explanation: