## 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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ReplyDeleteIf you are preparing for a competitive exam its important for you to make your speed in mathematics. For this, you have to make your strength in simplification because if you are good at simplification then you can solve questions quickly. For solving "number series" there is a number of tricks but your calculation must be fastest for that. If you want to increase your calculation speed you have to do practice and follow short tricks of calculation.

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