I need help on these questions...?

Question

I can't figure out these problems:

Find the next 2 terms:

1, 3, 4, 7, 11, 18, 29, 47, ......

Write down the nth term of the sequence:

2, 5, 10, 17, 26, .........

Thanks

Answer 1

Find the next 2 terms:

1, 3, 4, 7, 11, 18, 29, 47, ......76

Write down the nth term of the sequence:

2, 5, 10, 17, 26, .........37

Answer 2

First, write out the diffrences between each of the numbers, so for the first one:

2, 1, 3, 7, 11, 18

Now write out the diffrences between the diffrences:

-1, 2, 4, 4, 7

So there is no distinct pattern there.

What you should do now is look for relationships between the numbers themselves e.g Prime numbers, squares. Try things like multiplying the 1st and 2nd term to see if it equals the 3rd term.

Here you should notice that the first term + the second term =  the 3rd term, and the 2nd term + the 3rd term = the 4th term.

So that one is easy enough.

2/ Again start writing out the diffrences:

3, 5, 7, 9

2, 2, 2, 2

so from that we can assume the next term will be +2 from 9 and the term after that will be +4 from 9.

The formula for the nth term is n² + 1 in question 2 in case your intrested.

Answer 3

The sequences seem to be neither G.P nor A.P..may be harmonic progression I think...

Answer 4

I have the first one. You add the last two numbers together (eg- 1 + 3=4. 4 + 7=11. 11+18=29. 29 + 47= (76). I'll let you work the last one out. It's easy.

The second one...

Not sure, to be honest. You'll have to get a better man than I am, gunga din!

Answer 5

For the first one:

1, 3, 4, 7, 11, 18, 29, 47

1 and 3 are the first numbers, then you add them up:

3+1 = 4

Then, you add the last number of the sequence (3) to your addition (4)

4+3 = 7

Last number (4) to addition (7)... and so on

7+4 = 11

11+7 = 18

18+11 = 29

29+18 = 47

47+29 = 76

76+47= 123

The next two terms are 76 and 123.

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Second one

nth term refers to infinite, so you need to see what's going on wiith the sequence

1) 2 + 3 = 5 ----- 2+(2+1)=5

2) 5 + 5 =10 ----- 2+(2+1)+(2+1+2)=5

3) 10 + 7 = 17 ----- ((2+(2+1)+(2+1+2))+(2+3+2)= 17

4) 17 +  9 = 26 ----- ((2+(2+1)+(2+1+2)+(2+3+2)) + (2+5+2) = 26

As you can see, we begin from two, then add up the next odd number (3). Then, to that addition (5) we add up the next odd number (5). We continue...

So, next will be

26 + 11 = 37 ----- ((2+(2+1)+(2+1+2)+(2+3+2)+(2+5+2)) + (2+7+2) = 37

37 + 13 = 50 ----- ((2+(2+1)+(2+1+2)+(2+3+2)+(2+5+2)+(2+7+2... + (2+9+2)= 50

and so on

I would say

hehe

2 + (2+1) +SUM (sigma) (n=0 down) (n up) (4+n). N (belongs to) odd numbers (1, 3, 5,...)

Hope that works :S