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!
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
Hello dizzycarlyThe 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 $\displaystyle \tfrac56:1$.)
Grandad