Q4.

Here are the first 5 terms in a sequence.

3

12

48

192

768

(a) Find an expression, in terms of n, for the nth term of this sequence.

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(2)

Ben says that 78 6432 is in the sequence.

(b) Is Ben right?

You must explain your answer.

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Guest Jan 3, 2018

#4**+2 **

1)

The first question is an example of a geometric progression since the given sequence has a constant ratio of 4. This can be determined by finding the quotient of any term of the sequence and the immediately preceeding term. The general structure of geometric progressions are of the following:

\(a_n=a_1*r^{n-1}\)

n = the nth term of the given geometric progression

r = the common ratio

a_{1}= the first term of the sequence

Knowing all of this, we can substitute a few values into this formula.

\(a_n=3*4^{n-1}\)

You will see that this formula generates the numbers given in the sequence in its given position.

2)

In order to determine if a number, like 786432 appears in this geometric progression, let's plug it in for \(a_n\).

\(786432=3*4^{n-1}\) | First, divide by 3 on both sides. |

\(262144=4^{n-1}\) | It is not necessary to solve for n to determine whether or not this number appears in this sequence. All we need to determine is that the number is divisible by the common ratio, 4 in this case. This number certainly is since the last two digits, 44, is divisible by 4, so the entire number is divisible by 4. This is valid since we are determining that this number fits the set common ratio, which it does. |

TheXSquaredFactor Jan 3, 2018