## What is next terms in the series ?

##
**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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