Find the patterns for these please?

Question

These are the ones I'm stuck on.... GETTING REALLY TIRED. PLEASE HELP OR TRY TO EXPLAIN. DONT TELL ME TO DO MY OWN HOMEWORK, THATS WHY I ASK THE QUESTIONS I DON'T GET TY! **NO SILLY ANSWERS**
a) 2, 5, 10, 17, 26... Next 3 Numbers?
b) 0, 3, 8, 15, 24... Next 3 #'s?
c) 3, 15, 35, 63... Next 3 #'s?

Other Questions:
Describe how you identify a number pattern.

The 17th and 37th term? of c)

Answer 1

A and B are the same pattern, just off by 2.
5 -2 = 3
10 - 5 = 5
17 - 10 = 7
26 - 17 = 9

Thus, the next three numbers should go up by 11, 13, and 15, respectively.

C is similar, as the terms increase by 12, then 20, then 28. The next three terms should go up by 36, then 44, then 52 (increasing by eight more each time).

Answer 2

a) 2, 5, 10, 17, 26, 37, 50, 65

2+3=5
5+5=10
10+7=17 and so on...
each time you add 2 to the difference of the previous two integers in the series (add 3, add 5, add 7, add 9...)
in a formula it would look something like i_[n+1]= (i_[n] - i_[n-1]) + 2 whre the "_[ ]" denotes a subscript

b) 0, 3, 8, 15, 24, 35, 48, 63
0+3=3
3+5=8
8+7=15 and so on...

same pattern as a)

c) 3, 15, 35, 63, 99, 143, 195...

same pattern again except this time we're using 8 insead of 2
3+12=15
15+20=35
35+28=63 and so on....

notice the 12, 20, 28, ... just going up by 8 each time such that:
i_[n+1]= (i_[n] - i_[n-1]) + 8

The trick to all of this is just finding the pattern in the pattern. In each of these 3 cases you just look at the difference between the numbers and in each case they simply increment by 2 for questions a and b or increment by 8 as in question c. Other patterns to look for would be multiplication or something like that. Notice the following: 3, -6, 12, -24, 48... each time we are just multiplying by -2 so we have i_[n+1] = i_[n] * 2

or maybe we have: 0, 3, 9, 18, 30...

each time we increment by 3*n
0+3*1=3
3+3*2=9
9+3*3=18
18+3*4=30 and so on...

i_[n] = i_[n]+3*n

Hope it helps you to see the patterns, just remember that the pattern is what is happening with the difference of the numbers in the series. Good luck!

Answer 3

a) adding odd numbers
2 5 10 17 26
+3 +5 +7 +9
next three numbers =
26 37 50 65
+11 +13 +15
b) same thing adding odd numbers
0 3 8 15 24 so 35 48 6 3
+3 +5 +7 + 9 +11 +13 15
c)can't help you there

Answer 4

a) 2 + 3 = 5, 5 + 5 = 10, 10 + 7 = 17, 17+ 9 = 26

You're adding what you added to the previous number plus two.

So the next three numbers are:

26 + 11 = 37
37 + 13 = 50
50 + 15 = 65

b) 0 + 3 = 3, 3 + 5 = 8, 8 + 7 = 15, 15 + 9 = 24
Same thing here.

24 + 11 = 35
35 + 13 = 48
48 + 15 = 63

c) 3 + 12 = 15, 15 + 20 = 35, 35 + 28 = 63
Here you're adding what you added to the previous number plus eight.

63 + 36 = 91
91 + 44 = 135
135 + 52 = 187

Answer 5

2,5,10,17,26
+3, +5, +7, +9 +
2, 5, 10, 17, 26

You might notice a pattern forming from the + numbers as they are the odd numbers, you should be able to figure it out from that clue. And all this without me tell you the actual answer.

0,3,8,15,24

You might notice the same pattern there.

3,15,35,63

1x3, 3x5, 5x7, 7x9

Try that pattern for a idea to figure out the next numbers.

....... The way to discover the next number in a series is to start trying to find a pattern in the differences between the numbers in the series.

1,2,3,4,5 is a series where the difference between the numbers is +1 more than the one before it.

1, 2, 4, 7, 11 is a series where the difference between the numbers is another series +1,+2,+3,+4 etc. So the first step would be to just subtract the first number form the second and the second from the third and so on. Then see if there is a pattern forming in the results you get, if the numbers are very large and don't seem to make any sense try factoring the numbers and see if the patter exists in side the factors. As the series become more difficult your going to have to try combining both multiplication, addition, subtraction and division in to your problem solving.

Hope this helps in your studies.

Answer 6

a.) 37, 50, 65 the numbers are being adding up by odd intergers
5-2 = 3
10-5=5
17-10=7
26-17=9 so you would add

11 to 26, 13 to the next and 15 to the next

b. 35, 48, 63 the same goes for this one as problem (a)

3-0=3
8-3=5
15-8=7
24-15=9

so you would add 11 to 24, 13 to the next and 15 to the next number

c.) 99, 143, 195

these are being moved up my intergers of 8

15-3=12
35-15=20
63-35=28

do you see how they are adding 8 to the previous numbers addeum?

so now you would add 36 (28+8) to 63 and 44 to the next and 52 to the following

hope this helps.

Answer 7

a) adding consecutive odd numbers, +11, +13, +15 = 37, 50, 65
b) same here, +11, +13, +15 = 35, 48, 63
c) multiply first odd number by next odd number... 3, 3*5=15, 5*7=35, 7*9=63, so next three are 9*11=99, 11*13=143, 13*15=195

Answer 8

#1) 2 (+3) 5 (+5) 10 (+7) 17 (+9) 26 (+11) 37 (+13) = ____
Please look at pattern so you understand... each time you must add the next odd# in the parentheses. i left last one so you may add for 3rd number required.

Answer 9

a=2,5,10,17,26,37,50,65

b=0,3,8,15,24,35,48,63

and i am still trying c
it is really hard