If n is any natural number- then 9 n -5 n ends with-A- 5B- 8C- 3D- 6

The correct option is D 6 9^1=9 9^2=81 9^3=729 ∴9^n ends with either 9 or 1. Similarly, 5^n ends with only 5. When 9^n ends with 9, then 9^n 5^n ends with 4 a ...

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Standard X

Mathematics

Applications of HCF & LCM in Real-World Problems

If n is any n...

Question

If $n$ is any natural number, then $9^{n} - 5^{n}$ ends with:

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Solution

The correct option is
D

6
Given, $n$ is a natural number.
Now,
$9^{1} = 9$
$9^{2} = 81$
$9^{3} = 729$
$9^{4} = 6561$
$∴$ $9^{n}$ ends with either 9 or 1.
Similarly,
$5^{1} = 5 5^{2} = 25 5^{3} = 125$
$5^{n}$ ends with only $5$ .

When $9^{n}$ ends with 9, then $9^{n} - 5^{n}$ ends with $4$ as $9 - 5 = 4$
And, When $9^{n}$ ends with 1, then $9^{n} - 5^{n} = 81 - 25 = 56$ ends with 6 .

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Similar questions

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If n is any natural number, then 9n−5n ends with:

The correct option is D 6Given, n is a natural number.Now,91=9 92=81 93=72994=6561∴9n ends with either 9 or 1. Similarly, 51=552=2553=1255n ends with only 5. When 9n ends with 9, then 9n−5n ends with4 as 9−5=4 And, When 9n ends with 1, then 9n−5n=81−25=56 ends with 6 .

If $n$ is any natural number, then $9^{n} - 5^{n}$ ends with: