If 10n + 3.4n+2 + k is divisible by 9 for all n ϵ N, then the lea

1.	If 10n + 3.4n+2 + k is divisible by 9 for all n ϵ N, then the least positive integral value of k isA. 5B. 3C. 7D. 1
Answer» A. 5 Given; Given; P(n): 10ⁿ + 3.4ⁿ⁺² + k is divisible by 9. P(1) = 10 +3.4³ + k = 202 + k For this number to be divisible by 9; sum of its digits should be 9 or multiples of 9. ⇒ 2 + 2 + k = 9 ∴ k = 5

If 10n + 3.4n+2 + k is divisible by 9 for all n ϵ N, then the least positive integral value of k isA. 5B. 3C. 7D. 1

Answer»

A. 5

Given; Given; P(n): 10ⁿ + 3.4ⁿ⁺² + k is divisible by 9.

P(1) = 10 +3.4³ + k = 202 + k

For this number to be divisible by 9; sum of its digits should be 9 or multiples of 9.

⇒ 2 + 2 + k = 9

∴ k = 5