If the greatest divisor of 30 5^ 2 n +4 2^ 3 n is p, n N and that of 2^ 2 n+1 -6 n-2 is q, n N , then p+q=

Step-by-step solution

We have, 30 5^ 2 n +4 2^ 3 n Put Put aligned n & =1 30 25+4 8 & =750+32=782 782 & =2 23 17 aligned Put x=230 625+4 64=18750+256=19006 In Eqs. (i) and (ii), we get Greatest divisor =2 17=34 p=34 Now in 2^ 2 n+1 -6 n-2 Put n=1 8-6-2=0 Put n=2 32-12-2=18 Put n=3 128-18-2=108 Greatest divisor =18 aligned q & =18 p+q=34+18 & =52 aligned