Question

1, 3, 11, 43, 171, 683, what's next in this sequence?

Answer 1

Answer:

2731

Step-by-step explanation:

3 - 1 = 2 = 2^1

11 - 3 = 8 = 2^3

43 - 11 = 32 = 2^5

171 - 43 = 128 = 2^7

683 - 171 = 512 = 2^9

Following the pattern, add 2^11 to 683.

683 + 2^11 = 683 + 2048 = 2731

Answer 2

Hi,

We have the sequence 1 , 3 , 11 , 43 , __.

Let us say  $a_{1}=1 , a_{2}=3 , a_{3}=11 , a_{4}=43$  and it is required to find out $a_{5}$ .

As, we can see the pattern from the given four terms that,

$a_{2}=a_{1}+2$ i.e. $a_{2}=a_{1}+2^{1}$

$a_{3}=a_{2}+8$ i.e. $a_{3}=a_{1}+2^{3}$

$a_{4}=a_{3}+32$ i.e. $a_{4}=a_{1}+2^{5}$

Since, the next term is obtained by adding the previous terms by odd powers of two.

Therefore, $a_{5}=a_{4}+2^{7}$ i.e. $a_{5}=a_{4}+128$ i.e $a_{5}=43+128$ i.e. $a_{5}=171$

So, $a_{5}=171.$

Hence, the next term of the sequence is 171.

Let us say  $a_{1}=1 , a_{2}=3 , a_{3}=11 , a_{4}=43$, $a_{5}$ $= 683$ and it is required to find out $a_{6}$.

Therefore, $a_{6}=a_{5}+2^{9}$ i.e. $a_{6}=a_{5}+512$ i.e $a_{6}=683+512$ i.e. $a_{6}=1195$

So, $a_{6}=1195.$

Hence, the next term of the sequence is 1195.