Math Is Fun Forum

place value

Member

Registered: 2015-12-13

Posts: 1

Number Sequence, Is there a relevant formula? Please show me the steps

hello everyone,

I am preparing for an exam. In brief, my exam practice book shows the following number sequence:
20, 30, 50. And asks what is the next number in the sequence?
The answer that the book gives is 80.

Years ago, when I took a math class, i remember there being a formula for arithmetic and geometric number sequence problems. Now, as I look at these formulas I can't seem to understand which of these formulas applies here. I understand that there is a steady increase on top of the cumulative total.

Term 1     Term 2              Term 3                Term 4                    so on and so forth ...     
                term 1 + 10       term 2 + 20         term 3 + 30
= 20           = 30                  = 50                    = 80

   
My question, is there a formula that would tell me the 300th term in this sequence?

your help is much appreciated,
thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Number Sequence, Is there a relevant formula? Please show me the steps

Hi;

There are lots of ways to come at a problem like this. The answer you want is

where n is the term number. If you plug in n = 1 ( first term ) you will get 20 etc.

It should be mentioned that although the book answer is 80 for the next term this is completely arbitrary. There is no reason why the next number should not be 156 or e or -1200.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Number Sequence, Is there a relevant formula? Please show me the steps

hi place value

Welcome to the forum.

20, 30, 50,   ....

You're right that it isn't an arithmetic or geometric sequence.

I think it is unreasonable to expect anyone to get the general rule from so few terms.  bobbym has provided a quadratic formula that works.

But other rules will also work, such as

This is the rule for the Fibonacci sequence and it works here too.

20+30 = 50
30+50 = 80

A general formula for that does exist but it is very complicated so predicting the 300th term without slogging through all the terms in between would be hard to get.

What is the exam ?  Maybe that will give us a clue.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Number Sequence, Is there a relevant formula? Please show me the steps

I don't have a teacher's take on this, but I don't find it too unreasonable in the scheme of bad exam questions. I would have arrived at the same answer bobbym gave, probably because I would be checking specific kinds of rules instead of using my imagination xD

Incidentally, that rule has a minimum of 18.75 when n = 0.5, and

Incidentally again, the rule for the Fibonacci sequence is: ((1/2*(1+√5))^n - (1/2*(1-√5))^n) / √5
While probably difficult to find, it is not all that intimidating to look at (: I don't know yet about the similar rule for this sequence involving √5 though. However, spreadsheets make this process quite simple, if you don't mind approximate answers as the numbers get very long (or spending time manipulating the result to see further decimal places).

I tried the process term(n+1) = term(n) + term(n-1). It says the 300th term will be about 5.8181 * 10^63, or 5.8181 vigintillion. Yikes

Last edited by Relentless (2015-12-18 16:37:10)