Question

Here is a sequence of numbers: 64,49,36,25,16. What is the name given to these numbers

Answer 1

These are squares of numbers 8 to 4.

Explanation:

The given sequence of numbers is given as:

64, 49, 36, 25, 16

First of all let us factorize each number:

`64 = 8 * 8\\49 = 7 * 7\\36 = 6 * 6\\25 = 5* 5\\16 = 4* 4\\`

We can see that every number is obtained by multiplying some other number by itself.

For example, 64 is obtained by multiplying 8 with itself i.e. 8 multiplied with 8.

49 is obtained by multiplying 7 with itself i.e. 7 multiplied with 7.

and so on.

So, each number is a square of some number.

The numbers are in decreasing order. (64 to 16)

i.e. we have square of numbers here.

Square of 8, square of 7, square of 6, square of 5, square of 4,

Generalizing the terms:

`a_n = (9-n)^2` where n is from 1 to 5

The name given to the sequence is:

Square of (9-n) where n is from 1 to 5.

OR

square of numbers, numbers from 8 to 4 in decreasing order.