Question

The Bird problem in can be slightly
changed as follows.
One bird said:
"We and we again, together with half of us and half of that, and
one more is a natural number"
Write all the possible number of birds, starting from the least. For each
of these, write the sum told by the bird also.
Find the algebraic expression for these two sequences.​

Answer 1

Answer:

Let the possible no of birds be x,

Therefore, according to given condition

$x+x+\frac{x}{2} +\frac{x}{4} +1 = N$

Where N is any natural number.

$\frac{4x+4x+2x+x}{4} =N$

⇒ 11x = 4N  

$x = \frac{4N}{11}$

Also, no of birds should also be a natural number, therefore N should be a multiple of 11, i.e. N = 11n for any natural no 'n'  

Hence possible values of N = 11, 22, 33…  

And possible values of x = 4, 8, 12, …

Algebraic expression for N is 11n

And  

For x is 4n.