Answer:
To determine the first term of the geometric progression, let's assume it is 'a'. From the given information, we know that:
Second Term = a + 50
(n + 1)th Term = a + 56
We also have the formula for the nth term of a geometric sequence:
nth term = a * r^(n-1)
where 'r' is the common ratio between consecutive terms. Since the difference between consecutive terms remains constant, i.e., 50 for the second term and 56 for the (n + 1)th term, we can set up the equation:
a + 50 = a * r^1
a + 56 = a * r^2
Solve the equations simultaneously:
a + 50 = a * r^1 => a - 50/r = 0
a + 56 = a * r^2 => a - 56/r = 0
Adding the two equations, we get:
2a - (50/r + 56/r) = 0
2a - (50 + 56)/r = 0
Simplifying the equation further, we obtain:
2a - (106/r) = 0
Now, solve for 'a':
2a - (106/r) = 0
2a = (106/r)
=> 2a = 106/r
The value of 'a' depends on the value of 'r', so we cannot determine its exact value without knowing 'r'. However, once we know 'r', we can calculate the value of 'a'.