Please help me with 7th sum (correct option is B)

Dear Student,
Please find below the solution to the asked query:

fn=10n+3.4n+2+5=10n+3.4n.42+5fn=10n+48.4n+5=1+9n+48.1+3n+5=1+nC1 9+nC2 92+....+nCn 9n+48 1+nC1 3+nC2 32+....+nCn 9n+5=1+nC1 9+nC2 92+....+nCn 9n+48 1+nC1 3+nC2 32+....+nCn 9n+5=nC1 9+nC2 92+....+nCn 9n+48nC1 3+nC2 32+....+nCn 9n+1+48+5=9nC1+nC2 9+....+nCn 9n-1+48×3nC1+nC2 3+....+nCn 3n-1+54=9nC1+nC2 9+....+nCn 9n-1+16nC1+nC2 3+....+nCn 3n-1+6Hence 9 is the largest integer for which divides fn for all nNOptionB

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