Question

if n is any natural number then the unit digit of 11^n-5^n is​

Answer 1

Question :-

• if n is any natural number then the unit digit of 11^n-5^n is ?

Solution :-

Let n = 1

Hence,

$11 {}^{n} - 5 {}^{n} = 11 {}^{1} - 5 {}^{1} = 6 \: \: \: ans$

Hence the unit digit of the given expression is= 6

Answer 2

Answer:

6

Step-by-step explanation:

Case 1 :- Let n is an even number .

n = 2, 4 , 6, 8, 10, 12 ..........

now,

take n = 2

11² - 5² = 121 -25 = 96 ends with 6

take n = 4

(11)⁴ - (5)⁴

= (11² + 5)²( 11² -5²)

= (121 +25)( 11-5)(11+5)

= 146 × 6 × 16 hence ends with 6

..............

......,....

hence, if we take n is an even number then, 11^n - 5^n ends with 6

Case2 :- Let n is an odd number .

n = 1, 3 , 5 , 7, 9, 11...........

take n = 1

11¹ - 5¹ = 11 -5 = 6 ends with 6

take n = 3

11³ - 5³ = (11 -5)(11² + 5² + 11×5)

= 96 × ( 121 +25 +55)

= 96*201 ends with 6

,..................

................

hence, if we take n Is an odd number then 11^n - 5^n also ends with 6.

now , by case1: and case2: we conclude that11^n -5^n ends with 6 when n is a natural number .

so, the answer is 6