Question

what are the next two terms 13, -5, -35, -77

Answer 1

so the next two terms are -57 and -149

Answer 2

thank you

Answer 3

they cannot be next two terms

Answer 4

?

Answer 5

this looks tough, @amistre64 may be able to help if hez free :)

Answer 6

wolfram saysm next two terms are -131, -197
but im not sure how to analytically get the answer

http://www.wolframalpha.com/input/?i=+13%2C+-5%2C+-35%2C+-77%2C+...

Answer 7

13, -5, -35, -77
-18 -30 -42
-12 -12 <-- this last row is a constant at -12

Answer 8

these are known as difference tiers, each row represents the difference of the 2 elements above it

if we can get down to a row thats constant, we can then develop a formula for any nth term

Answer 9

so -12,-12 is the next two terms

Answer 10

of course not ... but they do play a part in how we can construct the next 2 terms

Answer 11

13, -5, -35, -77 a
-18 -30 -42 b
-12 -12 c

c = -12

-42+c = b

-77 + b = a

Answer 12

-57,-149 ?

Answer 13

-57 is not correct for the next term since it is obviously bigger than -77 and the terms are getting smaller

Answer 14

but -149 is correct?

Answer 15

13, -5, -35, -77 a
-18 -30 -42 b
-12 -12 c

13, -5, -35, -77 -77-42-12
-18 -30 -42 -42-12
-12 -12 -12

Answer 16

13, -5, -35, -77 [-77-42-12] [-77-42-12-42-12-12]
-18 -30 -42 -42-12 -42-12-12
-12 -12 -12 -12

Answer 17

i get it, this is really cool method, thnks a lot @amistre64 :))

Answer 18

-131 and -197 as has already been presented :)

Answer 19

so its -131 and -197