Fun with Sequences

Number Theory Level 3

$2, 11, 22, 121, 1012, 2101, . . .$

What is the 9th term in this sequence?

The answer is 200222.

1 solution

Stephen Shamaiengar
Mar 2, 2014

One must realize that the only digits used are 0 to 2, so the sequence is in base 3. After converting to base 10, the sequence is simply $2^n$ , n being the term number. So the 9th term is $2^9$ = 512, and converted to base 3 for answer, $\boxed{200222}$

i don't get it.

JejeRem JereRem - 7 years, 2 months ago

Which part of it? It's simply a sequence of base 10 numbers converted to a different base.

Stephen Shamaiengar - 7 years, 2 months ago

Convert 2,4,8,16,32..... to base 3 (from base 10), and you'll get the same series as in the question.

Satvik Golechha - 7 years, 1 month ago

This is based on the concept of bases. According to that a valu can be experssed in different systems. For example decimal system which is commonly used used 10 digits (0-9). Binary uses only 2digits (0-1) , hex, hexdecimal, etc. The number of possible numbers is is known as base. Eg: decimal is base 10, binary is base 2. Interconvertions are also possible

Gowtham Amirthya - 7 years, 2 months ago

Fun with Sequences

The answer is 200222.

1 solution

0 pending reports