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How many terms are there in a G.P if a=8,an=1\512,r =1 \2

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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.

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