The given information is that a = 8, an = 1/512, and r = 1/2. We need to find the number of terms in the geometric progression (G.P).
In a geometric progression, each term is obtained by multiplying the previous term by a common ratio (r).
To find the number of terms, we can use the formula:
an = a * (r^(n-1))
Here, n represents the number of terms.
Plugging in the given values, we have:
1/512 = 8 * (1/2)^(n-1)
To solve for n, we can rewrite the equation using powers of 2:
1/2^9 = 2^3 * (1/2)^(n-1)
Now, we can equate the exponents:
-9 = 3 + (n-1)
Simplifying, we get:
-9 = n + 2
Subtracting 2 from both sides, we find:
n = -11
However, the number of terms in a geometric progression cannot be negative. Therefore, in this case, there are no terms in the geometric progression (G.P).
In summary, the given geometric progression with a = 8, an = 1/512, and r = 1/2 has no terms.