Question

Use inductive reasoning to find the ones digit of the number 250.

Answer 1

Answer:

Answer: Yes, and the units digit is 4. Every fourth power the units digit will be 6. So the units digit for 248 would be 6, and the units digit for 250 would be 4.

Step-by-step explanation:

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Answer 2

Inductive Reasoning

To find:

Ones digit of $2^{50}$

Explanation:

It is a method of logical thinking that combines observations and information collected from various experiments to reach the conclusion.

In this case, we can see  that

$2^1$ ends in 2

$2^2$ ends in 4

$2^3$ ends in 8

$2^4$ ends in 6

$2^{5}$ ends in 2

$2^6$ ends in 4

$2^7$ ends in 8

$2^8$ ends in 6

We can see that cycle repeats in the gap of 4.

Every forth power the unit digit is 6.

Since  $50 = ( 4$ × $12) + 2$

So the units digit for  $2^{48}$  would be 6, and the units digit for $2^{50}$  would be 4.

The last digit of $2^{50}$ is 4.

We can find the solution of this type of question using,

It is observed that  

unit digit of $2^n$ is 2 when n ≡ 1(mod4)  

unit digit of $2^n$ is 4 when n ≡ 2(mod4)  

unit digit of $2^n$ is 8 when n ≡ 3(mod4)  

unit digit of $2^n$ is 6 when n ≡ 0(mod4)  

∵50 ≡ 2(mod4)

Hence, unit digit of $2^{50}$ is 4.