Find the missing number.==> 3, 7, 23, x, 343, 1367

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the terms of the sequence given as 3, 7, 23, x, 343, 1367. This does not have a common ratio or a common difference.

Let's see what the difference between the terms is

7-3 = 4

23 - 7 = 16

1367 - 343 = 1024

If we see the difference 4 = 2^2 , 16 = 2^4, 1024 = 2^10

The difference between the nth term and the (n + 1)th term can be expressed as 2^2n

Applying the same rule x - 23 should be 2^6 or

x - 23 = 64

=> x = 87

To verify we see that 343 - 87 = 256 which is 2^8.

The term to be found is x = 87.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the sequence of numbers.

3, 7, 23, x, 343, 1367

We need to find the value of x.

Then we will need to determine the relation between the terms.

Let us determine the differences between each two consecutive terms.

==> 7-3 = 4   = 2^2

==> 23-7 = 16 = 2^4

==> x - 23 =  r1

==> 343-x = r2

==> 1367-343= 1024 = 2^10

Now we notice that the difference has a patterns such that an= 2^2n

Then , we notice that r1= 2^6 and r2= 2^8

==> x-23 = 2^6 = 64

==> x = 64+ 23 = 87

To check we will calculate using r2.

==> 343-x = 2^8 = 256

==> x = 343- 256 = 87

Then the missing number is x= 87.

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