5.-10. 20.-40 determine if arithmetic, geometrical or neither

Geometric progression.

Step-by-step explanation:

I suppose you mean this equation:

5, -10, 20, -40, ...

For a geometric progression, an n^th term is given by:

= × r

Where a is the first time, n is the term and r is the common ratio.

The common ratio here is -2 .

For instance to check the forth term;

= × -2  = 20 × -2 = -40

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)