What is the unit digit of $-18 + 18^2 - 18^3 + 18^4 - ...... - 18^{19} + 18^{20}$ ?

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Explanation

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Official Explanation

Official

To determine the unit digit of the expression, we need to evaluate -18 +

18^2

18^3

18^4

- ...... -

18^{19}

18^{20}

. The unit digit of all the bases is 8. The cyclicity of 8 is 4, meaning the unit digits will repeat every 4 terms. Therefore, we will have 5 complete cycles in this…

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Comments

PrakharJun 1, 2024

Tricky wording but good practice

AryamanOct 26, 2024

greatt question!

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).

What is the unit digit of −18+182−183+184−......−1819+1820-18 + 18^2 - 18^3 + 18^4 - ...... - 18^{19} + 18^{20}−18+182−183+184−......−1819+1820?