What are the next two numbers in the pattern, 5, -10, -20, -40?

1 Answer
Dec 17, 2017

Answer:

Expanding on the idea...

Explanation:

We can also formulate this

This is called a geometric sequence, where the next term can be obtained by multiplying the prior term by a paricular number, called a common ration...

So if #a# is our first term, and #r# is our common ration, then our sequence would look like...

#a,ar,ar^2,ar^3....#

This has an #nth# term of: #a*r^(n-1) # where the first term is at #n=1#

Your sequance is:

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

So #a = -5 and r = 2 #

#nth # term = # (-5)*2^(n-1) #

So our next terms our #n=5 # and then #n = 6 #

So hecne using the formula: -80, -160 are the next two terms

We can also take a sum of the first #n# terms, but thats a different story...!