Question

4 , 14 , 60 , 248 , ?​

Answer 1

SOLUTION

TO DETERMINE

4 , 14 , 60 , 248 , ?

EVALUATION

Here it is given that 4 , 14 , 60 , 248 , ?

Now

$\sf{4 = {4}^{1} - 0}$

$\sf{14 = {4}^{2} - 2 = {4}^{2} - {2}^{1} }$

$\sf{60 = {4}^{3} - 4 = {4}^{3} - {2}^{2} }$

$\sf{248 = {4}^{4} - 8 = {4}^{4} - {2}^{3} }$

So the series is of the form

$\sf{ {4}^{n} - {2}^{n - 1} }$

Where n = 1, 2 , 3, 4 ,....

So the next term is obtained by putting n = 5

Hence the required next term

$\sf{ = {4}^{5} - {2}^{4} }$

$= 1024 - 16$

$= 1008$

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