+0

how do you find a sequence repesents thit three different numbers like

+1
298
3

how do you find a sequence repesents thit three different numbers like

(4,12)

(5,36)

(6,108)

May 4, 2017

#1
+94526
+1

(x , y)

(4,12)

(5,36)

(6,108)

Note that we can write this as an exponential function  in the form :  y = a(b)^x

So we have :

12  =  a(b)^4     →   a  =  12 / (b^4)      (1)

36 = a(b)^5       (2)

Sub  (1)  into (2)

36 = (12 / b^4) b^5    simplify

3 =  b

Subbing this into (1), we have that   a =  12 / 3^4  =  12/81  =  4/27

So  the function is

y  = (4/27) (3)^x

May 4, 2017
#2
0

If you want to know what sequence the numbers form, then it is as follows:

4, 12, 5, 36, 6, 108, 7, 324, 8, 972.........etc.

First term goes up by 1, such as 4+1, 5+1, 6+1......etc.

Second term is multiplied by 3, such as 12 x 3, 36 x 3, 108 x 3 .......and so on.

May 4, 2017
#3
+2

There is insufficient information in the question,

the quadratic  \(\displaystyle f(x) = 24x^{2}-192x +396\)

fits the sequence just as well.

You need to be told what sort of function that you're looking for.

(It's also possible to find an infinite number of cubics, quartics ... etc. as well.)

May 4, 2017