Find an equation for the nth term in the following sequence:
2, 8, 32, 128,

Step-by-step explanation:

The sequence shown matches that of a geometric sequence of radius 4. To prove it, divide the term and check that

Then the formula that represents this sequence is:

Where is the first term of the series = 2 and is the radius of convergence = 4.

Then the equation is:

nth term of the sequence is or

Step-by-step explanation:

The given sequence is 2, 8, 32, 128, 512.........

Or we can rewrite the sequence as

Now the new form of sequence confirms that the sequence is an exponential sequence.

Therefore nth term of the sequence will be Or

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560