series question?

Question

a)1, 2, 3, 5, 16,_


b)1, 2, 3, 8,_, 224

Answer 1

a) 21
b) 27

Answer 2

For a) after the first three terms each term afterwards is the sum of the last two terms times the previous term. For example, 5 is (3+2)*1 and 16 is (5+3)*2. The next term in the series should be (5+16)*3, or 63.

For b) after the first two terms each term is the sum of the number from two terms ago and the product of the last two terms. For example, (1*2)+2=3 and (2*3)+2=8. The missing term is 27, because then (3*8)+3=27 and (8*27)+8=224.

Answer 3

for a, the answer is 42:
1, 2 and then
(1+2)*1 = 3
(2 + 3)*1 = 5
(5+3)*2 = 16
(16+5)*2 = 42

If I were to continue:
(42+16)*3 = 173
(173+42)*3 = 645
etc

for b then answer is 27:
1,2 and then
(1*2)+1 = 3
(2*3)+2 = 8
(3*8) + 3 = 27
(8*24)+8 = 224

Answer 4

16^2 - 5^2 = 231

3*8 + 3 = 27
8*27 + 8 = 224

Answer 5

Questions such as these are a form of 'mind reading' that I, as a mathematician, find kinda offensive. If I said what's the next number in the sequence 3,5,7,.... I could be thinking of the odd numbers, or the odd primes.

Essentially, the problem is: I give you f(1), f(2), f(3),... and you get to 'guess' what the function f is.

So what I usually do is stuff in any number I like (in this case, maybe a -3 for both of them) and then justifying the answer by working up the "LaGrange Interpolation Polynomial" which has exactly those values at 1, 2, 3, 4, etc.

You can find out about LaGrange at
http://en.wikipedia.org/wiki/Lagrange_polynomial

I claim that this shows a *much* deeper understanding of math (particularly the Fundamental Therom of Algebra) than playing 'mind reading' games and trying to 'guess' what some moron had in mind when they wrote the test.

For example: If I'm given the series 1,4,9, and asked for the next term, I might well say 1 and justify it because (after a wee bit of computation ☺) I can show that
-2.5x^3 + 16x^2 -27.5x + 15 takes on exactly those values.

-2.5*1^3 + 16*1^2 -27.5*1 + 15 = 1
-2.5*2^3 + 16*2^2 -27.5*2 + 15 = 4
-2.5*3^3 + 16*3^2 -27.5*3 + 15 = 9
-2.5*4^3 + 16*4^2 -27.5*4 + 15 = 1

The above also used to get me right up at the top of my math teachers shitlist in high-school


Doug

Answer 6

a) 21 - 1+2=3 ... 2+3=5 ... 16+5=21

Answer 7

a) 63
the series adds the two previous numbers and then multiplies it by the number three spots ahead of it.
(1+1)x1=2
(2+1)x1=3
(3+2)x1=5
(5+3)x2=16
(16+5)x3=63

b) 27
the series builds by multipling the two previous numbers together and then adding the lower of the two to the total
(1x2)+1=3
(2x3)+2=8
(3x8)+3=27
(8x27)+8=224

Answer 8

a 21

Answer 9

)1, 2, 3, 5, 16,_ 26, 36, 46


b)1, 2, 3, 8,_, 224 __ 225, 226, 227, 232

Answer 10

a)
16=(5+3)*2
5=(3+2)*1 etc so:
n=[(n-1)+(n-2)]*(n-3) so the next number is (16+5)*3=63
b) don't know yet, I don't understand the underline there, if you edit your question maybe I find out
ps: no need to...

Answer 11

A) 5+16=21
B) no clue