if p(n); 2*4^(2n+1)+3^(3n+1) is divisible by k for all n belongs N then find the value of k

Dear Student, 
Solution)
For n=1,P1=2×42+1+33+1=2×43+34=128+81=209For n=2,P2=2×44+1+36+1=2×45+37=2048+2187=4235As, HCF209, 4235=11So, 2×42n+1+33n+1 is divisible by 11.Hence, the value of λ is 11.
​​​​​​(Here λ=k)
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