Question

What will be the last digit of the expansion of 237⁹³⁷?

• A. 1
• B. 9
• C. 3
• D. 7

Answer 1

The Correct Option is D

Last Digit Calculation of 237937

Step 1: Analyze the Last Digit of 237937 

To find the last digit of 237937, we only need to consider the last digit of 237, which is 7.

Therefore, we are interested in finding the last digit of 7937.

Step 2: Identify the Pattern in Powers of 7

The powers of 7 follow a pattern in the last digits:

• 7^1 = 7 (last digit = 7)
• 7^2 = 49 (last digit = 9)
• 7^3 = 343 (last digit = 3)
• 7^4 = 2401 (last digit = 1)

The cycle of last digits of powers of 7 is: 7, 9, 3, 1, and it repeats every 4 terms.

Step 3: Determine the Position of 937 in the Cycle

Now, we need to determine the position of 937 in this cycle:

\[ 937 \mod 4 = 1 \]

This means the last digit of 7937 will be the same as the last digit of 7^1, which is 7.

Final Answer:

The last digit of 237937 is 7.

Conclusion:

The correct answer is (d) 7.