A number theory problem by Kamala Ramakrishnan

Number Theory Level 2

What is the units digit of the following pattern:

3 1 + 3 2 + 3 3 + … + 3 500 3^{1}+ 3^{2} + 3^{3} + \ldots + 3^{500}


The answer is 0.

Kamala Ramakrishnan by Kamala Ramakrishnan , 50, India

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3 solutions

For every four times 3 is raised, the sum remains 0.

Since 500 is divisible by 4, the units digit of the sum is 0.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

The cycle is 3 units long.......

Krishna Viswanathan - 6 years, 11 months ago
Shreya R
Oct 24, 2014

3 has the cyclicity of 4. Since 500/4 = 0, the units digit is 0.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
William Isoroku
Aug 1, 2014

3^(4x), for any positive integer x), the number will have a 0 in its units digit. Since 500 is divisible by 4, it leaves no remainder, so 0 times any number is 0.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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