## What is next terms in the series ?

Let us solve next number in sequence puzzle
15,29,56,108,208,????
Here 1st term is 15, To find out 2nd term if we multiply the 1st term With 2 and subtract 1 from it, i.e (15 *2) -1  = 29
To find 2nd term we have to multiply the previous term with 2 and subtract 2 (double the previous time) from it
I.e 29*2 - 2 = 56
To find 3rd term we have to multiply the previous term with 4   and subtract 2  (double the previous time) from it
I.e 56*2 - 4 = 108
To find 4th term we have to multiply the previous term with 8 (double the previous time) and subtract 2 from it
I.e 108*2 - 8 = 208
Similarly 5th term can be calculated as
multiply the previous term with 2 and subtract  subtract 2 (double the previous time) from it
I.e 208*2 - 16 = 400
Next term 400*2 - 32 = 768

Next term  768*2 - 64 = 1472
Next term  1472*2 - 128 = 2816
Or we can write it in another form as follows
15+(15–1) = 29
29+(29–2) = 56
56+(56–4) = 108
108+(108–8) = 208
208+(208–16) = 400
400+(400–32) = 768

768+(768–64= 1472

1472+(1472-128) =2816

And similarly this trend follows

## What’s the next number in the sequence 0, 2, 6, 12?

We can get the answer in two  ways

### 1st way

1 * (1–1) = 0 ( 1st term)

2 * (2–1) = 2 (2nd term)

3 * (3–1) = 6 (3rd term)

4 * (4–1) = 12 (4th term)

5 * (5–1) = 20 (5th term)

Next term must be  20
Similarly
6 * (6–1) = 30  (6th term)

7 * (7–1) = 42  (7th term)

### 2nd Way

1^2 –1 = 0

2^2 – 2 = 2

3^2 – 3 = 6

4^2 – 4 = 12

5^2 – 5 = 20
Next term must be  20
Similarly

6^2 – 6 = 30

7^2 – 7 = 42

## Can you solve this  Series: 30, 31, 28, 33, 26, 35, … What number should come next?

We can split this sequence into two series by picking alternate numbers from the given sequence.
30, 31, 28, 33, 26, 35, …
1st  one is 30,  28, 26, … and 2nd one is  31, 33,  35, …
Now after careful analysing the 1st sequence ,it next terms should be  with decrease of  2 ,we get other terms as follows
30,  28, 26, 24,22,20 …
And after careful analysing the 2nd  sequence ,it next terms should be  with increase of  2 ,we get other terms as follows
31, 33,  35, ,37,39,41…

26-2 = 24.
So the text terms should be 30, 31, 28, 33, 26, 35, 24,37,22

24 is the next number in the required sequence

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