Question

2,6,10,14,18,22,26,30,34,38,42,46,50,54,58..and any 3 numbers and get 60 as the sum?

Answer 1

The expression is impossible.

Step-by-step explanation:

The above series is given as the nth term being:

$a_{n}=2(2 n-1)$

Thus, it is nothing but twice the series of odd numbers.

Now we need the sum of any three of the given series as 60

Let is keep the three numbers as $a_{x}, \ a_{y}, \ and \ a_{z}$

Thus,

$60=a_{x}+a_{y}+a_{z}$

Which can be simplified as:

$60 = 2(2x-1) + 2(2y-1) + 2(2z-1)$

Which can be simplified as:

$2 \times 30 = 2[(2x-1) + (2y-1) + (2z-1)]$

This results as:

$30 = (2x-1) + (2y-1) + (2z-1)$

Which is nothing but a sum of three odd numbers.

Now by mathematical principles, sum of three odd numbers results in an odd number.

Thus, the above expression is impossible to obtain given that there doesn’t exist any combination of odd number that can add up to 30 that is an even number.