Problem 2 · Find a last-digit cycle · 3 points
Made by AI and not reviewed by a real person.
What is the last digit of 2^2026 + 2^2027?
- 6
- 8
- 0
- 4
- 2
Show a hint
- Write down the last digit each time you multiply a power of 2 by 2. What happens if you keep going?
- Once the last digits repeat, use the exponents to find where each power falls in the cycle.
Show the answer and solution
Answer: E — 2
The last digits of powers of 2 repeat in a cycle: 2, 4, 8, 6. Since 2026 leaves remainder 2 when divided by 4, 2^2026 ends in 4. The next power ends in 8, and 4 + 8 = 12, so the sum ends in 2. The tempting 8 is the last digit of 2^2027 alone, not of the sum.