Question

Identify the 10th term for the sequence: 12,6,3,1.5...?

Answer 1

@trish what can we divide 12 by to get 6?

Answer 2

@Hero 0.5

Answer 3

Actually you divide 12 by 2 to get 6.

Answer 4

You can multiply by 0.5 to get 6 as well.

Answer 5

From my perspective, dividing by 2 is easier than multiplying by decimals.

Answer 6

@Hero when I do that both ways I'm getting a long decimal answer and I'm pretty sure it's not the answer

Answer 7

But I understand why you did it. Neverthless it should be obvious how to get to the tenth term.

Answer 8

Okay, so let's do it one step at a time.

Answer 9

I'll show you how it is easy. You just have to be comfortable converting between fraction and decimal.

Answer 10

So let's start with 1.5

Remember, to read 1.5 you say one AND five tenths which we can re-write in fraction form as \(1 + \dfrac{5}{10}\) but reduces to \(1 + \dfrac{1}{2}\)

Answer 11

Now suppose you take \(1 + \dfrac{1}{2}\) and multiply that by \(\dfrac{1}{2}\). If you do that you get \(\dfrac{1}{2} + \dfrac{1}{4}\) which adds to \(\dfrac{3}{4}\) or \(0.75\) in decimal.

Answer 12

Now that's our fifth term. Since we have \(\dfrac{3}{4}\) and need to get the sixth term, all we have to do is multiply \(\dfrac{3}{4}\) by \(\dfrac{1}{2}\) again to get the next term

Answer 13

@Hero as a fraction I got 3/128

Answer 14

Taking another angle at this, \(1.5\) is \(\dfrac{3}{2}\) in fraction form. You can multiply that by \(\dfrac{1}{2}\) to easily get \(\dfrac{3}{4}\)

Answer 15

Since \(\dfrac{3}{2} \times \dfrac{1}{2} = \dfrac{3}{4}\)

Answer 16

@Hero yes I understand the process but I'm hesitant that my answer is incorrect

Answer 17

Okay, so the pattern is \(a_{n-1} \times \dfrac{1}{2} = a_n\)

Let:
\(a_1 = 12\)

\(a_2 = 6\)

\(a_3 = 3\)

\(a_4 = \dfrac{3}{2}\)

Answer 18

Then
\(\begin{align*}a_5 &= a_4 \times \dfrac{1}{2} \\&= \dfrac{3}{2} \times \dfrac{1}{2} \\&= \dfrac{3}{4}
\end{align*}\)

Answer 19

So \(a_5 = \dfrac{3}{4}\)

Answer 20

To get \(a_6\) do the same thing.

Answer 21

\(a_6 = a_5 \times \dfrac{1}{2}\)

Answer 22

\(a_6 = \dfrac{3}{4} \times \dfrac{1}{2}\)

Answer 23

@Hero thanks so much I understand it now

Answer 24

Yeah but you never stated the tenth term.