The first term of a sequence is 2014. Each succeeding term is the sum of the cubes of the digits of the previous term. What is the 2014th term of the sequence?
This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
When posting on Brilliant:
Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
Markdown
Appears as
*italics* or _italics_
italics
**bold** or __bold__
bold
- bulleted - list
bulleted
list
1. numbered 2. list
numbered
list
Note: you must add a full line of space before and after lists for them to show up correctly
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
Math
Appears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3
2×3
2^{34}
234
a_{i-1}
ai−1
\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
\sin \theta
sinθ
\boxed{123}
123
Comments
Let's define this sequence as a1,a2,a3,...,a2014,... where a1=2014. The sum of the cubes of the digits of 2014 is 73. a2=73. The sum of the cubes of the digits of 73 is 370. a3=370. The sum of the cubes of the digits of 370 is 370 again. From this, we yield ak=ak+1 for k≥3. Therefore, a2014=a3=370. Therefore, the answer is 370.
First term is 2014,as per the given question the second term should be 2^3+1^3+4^3=73.Similarly third term will be 7^3 + 3^3 = 370.Now the rest of the terms as we go further comes out to be 370. So the ans is 370.
Here I term is 2014.
Second term is (2^3+0^3+1^3+4^3)=73.
Third term is (7^4+3^3)=370.
Now it is clear that ii and iii digits have only two natural no. And now if we sum the cube of digits then it will remain 370. Hence after iii term all the terms of this series will be 370. Hence answer is 370.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
Let's define this sequence as a1,a2,a3,...,a2014,... where a1=2014. The sum of the cubes of the digits of 2014 is 73. a2=73. The sum of the cubes of the digits of 73 is 370. a3=370. The sum of the cubes of the digits of 370 is 370 again. From this, we yield ak=ak+1 for k≥3. Therefore, a2014=a3=370. Therefore, the answer is 370.
Log in to reply
That is an Armstrong number. :-)
nice
An elegant solution.
1st term =2014
2nd term =73
3rd term =370
4th term =370
. . .
Same goes on and 2014th term =370
First term is 2014,as per the given question the second term should be 2^3+1^3+4^3=73.Similarly third term will be 7^3 + 3^3 = 370.Now the rest of the terms as we go further comes out to be 370. So the ans is 370.
370
Here I term is 2014. Second term is (2^3+0^3+1^3+4^3)=73. Third term is (7^4+3^3)=370. Now it is clear that ii and iii digits have only two natural no. And now if we sum the cube of digits then it will remain 370. Hence after iii term all the terms of this series will be 370. Hence answer is 370.
370
Here 2014=2^3+1^3+4^3=73 Second term =7^3+3^3=370 Third term=3^3+7^3=370 Therefore k>=3. Then a=370
370
370
370
370
370
370
370 :).
370
the answer is 370 because all the terms after the third term are 370
370