1. ## confusing >.<

I am really stuck on a question..

(Q) Find x from the following:

34.56, x, 24, 20.

The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

Thanks if you can show me how to do it!

2. Originally Posted by dizzycarly
I am really stuck on a question..

(Q) Find x from the following:

34.56, x, 24, 20.

The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

Thanks if you can show me how to do it!
Could you please write the problem exactly as it appears in the book? This would help me to better understand the problem.

Do you mean $\displaystyle T_n=a+(n-1)d$ or $\displaystyle S_n= \frac{n}{2}[2a+(n-1)d]$

If so, what do t, s, a, and d represent?

3. Originally Posted by dizzycarly
I am really stuck on a question..

(Q) Find x from the following:

34.56, x, 24, 20.

The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

Thanks if you can show me how to do it!
The two formulas you wrote are for use with arithmetic sequences, but the sequence you wrote is a geometric sequence.

In any event, x = 28.80 because the ratio between two consecutive terms is constant:
$\displaystyle \frac{34.56}{28.8} = \frac{28.8}{24} = \frac{24}{20} = 1.2$.

01

4. Originally Posted by yeongil

In any event, x = 28.80 because the ratio between two consecutive terms is constant:
$\displaystyle \frac{34.56}{28.8} = \frac{28.8}{24} = \frac{24}{20} = 1.2$.

01
Dude, you're like some kind of wizard.

5. ## Ap/gp

Hello dizzycarly
Originally Posted by dizzycarly
I am really stuck on a question..

(Q) Find x from the following:

34.56, x, 24, 20.

The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

Thanks if you can show me how to do it!
The formulae you quote are related to Arithmetic Progressions - where the differences between consecutive terms are equal. The difference between $\displaystyle 24$ and $\displaystyle 20$ is $\displaystyle -4$, and obviously this can't be the difference between $\displaystyle 34.56$ and $\displaystyle x$, and $\displaystyle x$ and $\displaystyle 24$.

So we must look elsewhere.

In fact, this is a Geometric Progression, where the ratio of consecutive terms is constant. You do it like this:

The ratio of $\displaystyle 24$ to $\displaystyle 20$ is $\displaystyle \frac{24}{20} : 1 = 1.2:1$. In other words, we must multiply $\displaystyle 20$ by $\displaystyle 1.2$ to make $\displaystyle 24$. If this sequence is a GP, we shall be able to multiply $\displaystyle 24$ by $\displaystyle 1.2$ to get $\displaystyle x$, and then multiply $\displaystyle x$ by $\displaystyle 1.2$ to get $\displaystyle 34.56$. And this works!

Try it out: $\displaystyle 24\times 1.2 = 28.8$, and $\displaystyle 28.8 \times 1.2 = 34.56$.

So $\displaystyle x = 2.8$.

(In fact, the common ratio of a GP is the ratio that will take you from left to right through the sequence of numbers; in this case that's the ratio the other way round; i.e. $\displaystyle 20:24$, or $\displaystyle \tfrac56:1$.)