Question

Which number comes next in the series: 5, 16, 49, 104,?

Answer 1

Answer:

The missing number in the given series is found to be 181.

Step-by-step explanation:

The series given to us in the problem is: 5, 16, 49, 104, __.

On carefully observing the pattern in the series, we can tell that the series is progressing in the odd multiples of 11. Representing the pattern, we can say:

$a_1=a=5$

$a_2= (11\times1)+a_1\\a_2=(11\times1)+5=16$

$a_3= (11\times3)+a_2\\a_3=(11\times3)+16=49$

$a_4= (11\times5)+a_3\\a_4=(11\times5)+49=104$

Following the same trend we can easily say that:

$a_5= (11\times7)+a_4$

Substituting the known information, we get:

$a_5= (11\times7)+104$

Or we can say:

$a_5=104+77$

which gives us:

$a_5=181$

Thus, the missing term in the given series is found to be 181.

Answer 2

The difference between the adjacent numbers is an odd multiple of 11. That is

$16-5=11=11\times 1\\49-16=33=11\times 3\\104-49=55=11\times 5$

So next should be

$x-104=77=11\times 7$

so the number $x=77+104=181$

so the series is $5,16,49,104,181$