Which term of the G.P. 2, 8, 32,… is 131072?

To find which term of the geometric progression (G.P.) 2, 8, 32,... is 131072, we will use the formula for the nth term of a G.P.:

T_n = a * r^(n-1)

Where:

T_n is the nth term,
a is the first term,
r is the common ratio,
n is the term number.
In the given G.P., we have:

a = 2 (the first term),
r = 8 / 2 = 4 (the common ratio).
We need to find the value of n when T_n = 131072.

Using the formula: 131072 = 2 * 4^(n-1)

Now, divide both sides by 2: 131072 / 2 = 4^(n-1) 65536 = 4^(n-1)

Next, express 65536 as a power of 4: 65536 = 4^8

Thus, we have: 4^(n-1) = 4^8

Since the bases are the same, we can equate the exponents: n - 1 = 8

Solving for n: n = 9

Therefore, the 9th term of the G.P. is 131072.