Select the correct answerHow many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?Options981011

The given sequence is a geometric progression (G.P.) where each term is multiplied by a common ratio to get the next term.

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

The formula to find the nth term (Tn) in a geometric progression is:

Tn = a * r^(n-1)

where:

• Tn is the nth term,
• a is the first term,
• r is the common ratio, and
• n is the number of terms.

We know that the nth term is 384, the first term (a) is 3, and the common ratio (r) is 2. We can substitute these values into the formula and solve for n:

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 n = 7 + 1 = 8.

So, there are 8 terms in the given geometric progression.