On Day 1, there are 256 apples on the tree. On each day after Day 1 until one apple is left the number of apples on the tree is half the number there were the day before. On Day ___, there will be only on apple on the tree

On day 9, there will be only one apple on the tree.

Step-by-step explanation:

Geometric Sequence

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

On day 1, there are 256 apples on the tree.

On the next day, there are half of the apples: 256/2=128 apples

On the next day, there are half of the apples: 128/2=64 apples

This is a geometric sequence with a common ratio of 1/2.

The general formula for the nth term of a geometric sequence is:

Where a1 is the first term and r is the common ratio. We need to find the value of n that results in only one apple in the tree:

Dividing by 256:

Since :

Applying exponents property:

Equating the exponents:

n - 1 = 8

n = 9

On day 9, there will be only one apple on the tree.

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