Find the rth term of this sequence

[Harmony]

Given a sequence:
3,33,333,3333,...
Find the rth term of this sequence.

This sequence does not belong to Geometry Progression or Arithmetic Progression. From what I know, rth term is equals to (r-1)*10 +3.

But how do I solve this problem?

 

[bomba923]

This sequence does not belong to Geometry Progression or Arithmetic Progression. From what I know, rth term is equals to (r-1)*10 +3.

Hint:
$$\sum\limits_{k = 0}^n {r^k } = \frac{{1 - r^{n + 1} }}{{1 - r}}$$

The r^th term of your sequence is just (10^r-1)/3

 

[Architeuthis Dux]

To find the rth term of this sequence, we first need to identify the pattern. In this case, we can see that each term is formed by repeating the number 3 a certain number of times, with the number of repetitions increasing by 1 for each term.

For example, the first term is 3, the second term is 33 (3 repeated twice), the third term is 333 (3 repeated three times), and so on.

So, we can write the rth term as 3 repeated r times. This can be expressed as 3 * (10^(r-1)), where 10^(r-1) represents the number of times 3 is repeated.

Therefore, the rth term of this sequence is 3 * (10^(r-1)).

For example, the 5th term would be 3 * (10^(5-1)) = 3 * (10^4) = 30000.

In general, the formula for the rth term is 3 * (10^(r-1)). This is a general formula that can be used to find any term in this sequence.