Question

If n is any natural number then 6" - 5" always and with
1
b
بابا
un
d
7​

Answer 1

Your Question:-

☆ If n is any natural number then $\tt 6^n - 5^n$ always end with:-

a) 1.

b) 2.

c) 5.

d) 7.

$\rule{200}2$

AnswEr:-

Your Answer is Option a.

ExplanaTion:-

Given natural number:-

$\tt\longrightarrow6 {}^{n} - 5 {}^{n}$

And we have to find out from which digit the number will always be end, in other words what will be its unit digit (i.e. the digit at one's place)

So here we know that, $\tt 6^n$ will always end with 6 for any natural number n.

For example,

Let n be 2 then,

$\tt\longrightarrow6 {}^{n} = {6}^{2} = 36 \\ \\ \tt which \: \: ends \: \: with \: \: 6.$

Let n be 3,

$\tt\longrightarrow6 {}^{3} = 36 \times 6 = 216. \\ \\ \tt which \: \: also \: \: ends \: \: with \: \: 6.$

Similarly $\tt 5^n$ will always end with 5 for any natural number n.

Therefore,

$\tt\mapsto(6 {}^{n} - 5 {}^{n} ) \: will \: \: always \: \: ends \: \: with: \\ \\ \tt\mapsto(6 - 5) \\ \\ \tt = 1.$

$\tt\therefore 6^n - 5^n$ will always end with 1 for any natural number n.

So the final answer is Option a).