Can you explain these number sequences.?

Question

I got the answers to them but i need somone to explain them in a way athat a 7th grader can understand. just explain what you have to do to get the number i i got

1) 2,7/2,5,13/2,8,19/2,11,25/2...

2)100,81,64,49,36,25,16,..

3)4096,1024,256,64,16,4,1

thanks.

Answer 1

1)This is an arithmetic progression, each element is the previous one + 3/2

2)This is the square numbers in from 100 and decreasing.  The next would be 9 then 4 then 1.

3)Each term here is the previous one divided by 4.  A geometric series with 1/4 as the common ratio.

Answer 2

1) they go up by 1.5  (7/2=3.5)

2)they are decreased by descending odd #s starting at 19

  100-19=81;  81-17=64; 64-15=49 ect....

3)# is divided by 4 to get next number

Answer 3

3 is the number divided by 4

Answer 4

what are you asked to find? the next number in the sequence or the equation that produces the numbers?

Answer 5

The first sequence:

1) 2, 7/2, 5, 13/2 ,8, 19/2, 11, 25/2...

is just counting by 1½, with every second number represented as a improper fraction. Without the improper fractions, it looks like this:

...2, 3½, 5, 6½, 8, 9½, 11, 12½...

The second sequence is 10², 9², 8², 7², 6², 5², 4²...

2)100,81,64,49,36,25,16,..

This last sequence is 2^12, 2^10, 2^8, 2^6, 2^4, 2^2, 2^1

3)4096,1024,256,64,16,4,1

[ The last one is not really much of a sequence! If it was 4096, 2048 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1 It would be the powers of 2, from 2^12 to 2^0. ]

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Answer 6

1) 3/2 separates each number 7/2 - 2 = 3/2, 25/2-11=3/2

2) they're all squares,where the number being squared decreases

3) previous number divided by 4

Answer 7

1.) start with 2, and keep adding 3/2. by putting them all in fraction from, with 2 in the denominator, it would appear: 4/2, 7/2, 10/2, 13/2 ...

2.) simply the square of numbers, starting with 10. so, 10x10=100, 9x9=81, 8x8=64 ...

3.) all of these numbers are powers of 4, starting with the 6th power and going down one each time. 4 to the 6th power (4x4x4x4x4x4) =4096, to the 5th power: 4x4x4x4x4=1024, to the 4th power: 4x4x4x4=256 ...