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If n  is any natural number then 6n - 5n always ends with
  • a)
    3
  • b)
    1
  • c)
    7
  • d)
    5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If n is any natural number then 6n - 5n always ends witha)3b)1c)7d)5Co...
Proof by Induction:
Let's assume that the statement is true for any natural number 'n', which means that 6n - 5n always ends with 1.

Base Case:
When n = 1,
6n - 5n = 6(1) - 5(1) = 1
So, the statement is true for the base case.

Inductive Hypothesis:
Assume that the statement is true for some natural number 'k', which means that 6k - 5k always ends with 1.

Inductive Step:
Now, let's prove that the statement is also true for 'k+1'.
(6(k+1) - 5(k+1)) % 10
= (6k + 6 - 5k - 5) % 10
= (k+1) % 10
= 1
Therefore, the statement is true for 'k+1'.

Conclusion:
Based on the principle of mathematical induction, the statement is true for all natural numbers. Therefore, the correct answer is option 'B' (1).
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Community Answer
If n is any natural number then 6n - 5n always ends witha)3b)1c)7d)5Co...
6n - 5n = 61 - 51 = 1
62 - 52 = 36 - 25 = 11 and so on
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