Question

Fill in the blanks in the sequence _,29,_,_,_,539, 1083

Answer 1

we are given the following sequence:

`_{}29,,,,539,1083`

To go from 539 to 1083 we multiply 539 by 2 and add 5, like this:

`1083=539*2+5`

Therefore, for a number in position "n", the formula for its value is:

`a_n=2a_(n-1)+5`

Solving we get:

`a_(n-1)=(a_n-5)/(2)`

Replacing the current value for 539 we get:

`a_5=(a_6-5)/(2)`
`a_5=(539-5)/(2)=267`

Now to find the 4th value:

`a_4=(a_5-5)/(2)`

Replacing:

`a_4=(267-5)/(2)=131`

For the third value:

`a_3=(a_4-5)/(2)`

Replacing:

`a_3=(131-5)/(2)=63`

The second value is already given as 29, therefore, the first value is:

`a_1=(a_2-5)/(2)`

Replacing:

`a_1=(29-5)/(2)=12`

Therefore, the sequence is:

`12,29,63,131,267,539,1083`