Find the first term and common difference of the arithmetic progression if the product of the first and last terms is 70 and second and third terms is 88
To find the first term and common difference of an arithmetic progression, we need two pieces of information: the product of the first and last terms (P) and the product of the second and third terms (Q).
Let's use the following variables:
- a: the first term
- d: the common difference
- n: the number of terms (unknown)
Given that the product of the first and last terms is 70, we have the equation:
a * (a + (n - 1)d) = 70 ------- Equation (1)
Similarly, given that the product of the second and third terms is 88, we can write:
(a + d) * (a + 2d) = 88 ------- Equation (2)
To solve these equations simultaneously, we can use the method of substitution.
Solving Equation (2) for a, we get:
a = (88 - 2d) / (1 + d) ------- Equation (3)
Substituting Equation (3) into Equation (1), we can solve for d:
((88 - 2d) / (1 + d)) * (((88 - 2d) / (1 + d)) + (n - 1)d) = 70
Now, we can solve this equation for d.
After finding the value of d, substitute it back into Equation (3) to find the value of a.
Note: The value of n is not provided, so we cannot determine the exact number of terms in the arithmetic progression with the given information.
You don't say how many terms there are. But we can do this just by inspection.
(a+d)(a+2d) = 88
a=5, d=3
5,8,11,14