Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

To find the 12th term of a geometric progression (G.P.), we are given that the 8th term is 192 and the common ratio is 2.

Step 1: Write down the given information: 8th term = 192 Common ratio = 2

Step 2: Use the formula for the nth term of a G.P.: nth term = a * r^(n-1)

Step 3: Substitute the given values into the formula: 8th term = a * 2^(8-1) = 192

Step 4: Simplify the equation: a * 2^7 = 192

Step 5: Solve for the first term (a): a = 192 / 2^7 = 192 / 128 = 1.5

Step 6: Use the formula to find the 12th term: 12th term = 1.5 * 2^(12-1)

Step 7: Simplify the equation: 12th term = 1.5 * 2^11 = 1.5 * 2048 = 3072

Therefore, the 12th term of the G.P. is 3072.