confusing series..!!!

Observe the series...the difference between any 2 consecutive terms in the series .

The series of difference is 14 , 39 , 75 , 124 ,......

So , the difference between the above series is 25 , 36 , 49 ,.......

In this way, if we solve ahead , we will get the 7th term as 1216 ....

P = 1216 mod 100 = 16.

$log_{2}$ (P x P ) = $log_{2}$ 256 = $\boxed{8}$

The differences is 14,39,75,124,... The differences in the differences is 25,36,49,...,which are 5,6,7... etc... raised to the power of 2. Thus next two differences of differences is 64 and 81.Thus next differences are 188 and 269 . And the next two terms are, 259+188 = 447 and 447+269 =716. 716 modulo 100 =16. Thus, log(2,16*16) = 4+4 =8.