How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?Options810119

A geometric progression (G.P.) is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

In this case, the common ratio (r) is 6/3 = 2.

The formula to find the nth term (Tn) of a G.P. is: Tn = a * r^(n-1), where a is the first term.

We know that the nth term is 384 and the first term (a) is 3. So, we can set up the equation as follows:

384 = 3 * 2^(n-1)

Divide both sides by 3:

128 = 2^(n-1)

Since 128 is 2 to the power of 7, we can say that 2^(n-1) = 2^7

Therefore, n - 1 = 7

Solving for n gives us n = 8.

So, there are 8 terms in the G.P. 3, 6, 12, 24, ... , 384. The correct option is 8.