Question

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

Answer 1

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.

Answer 2

2731

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