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melamori03 [73]
3 years ago
13

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

Mathematics
2 answers:
erastovalidia [21]3 years ago
7 0

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

zvonat [6]3 years ago
7 0

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.

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