Question

Problem 11.The sequence shown was formed by writing the first letter of the alphabet followed by writing the first two letters of the alphabet and continuing the pattern by writing one more letter of the alphabet each time. Continuing this pattern, what letter is the 280th letter in this sequence? A, A, B, A, B, C, A, B, C, D, A, B, C, D, E, .. . Problem 12.A sequenceof letters is formed by writing 1 A, 2 B’s, 3 C’s, and so forth, increasing the number of letters written by one each time the next letter of the alphabet is written. What is the 200th letter in the sequenc

Answer 1

Determining the value of k such that k(k+1)/2 is the largest triangular number less than or equal to 280.

Then, calculating the position of the letter within the kth group. The 280th letter is I.

Step-by-step explanation:

To find the 280th letter in the sequence, we can analyze the pattern and determine the letter at each position.

The sequence begins with the letter A, followed by the letters A and B. Then, it continues by adding one more letter of the alphabet each time. So, the third letter is C, the fourth letter is D, and so on.

This pattern suggests that we can determine the letter at position n by finding the value of k such that k(k+1)/2 is the largest triangular number less than or equal to n.

Then, the position of the letter within the kth group will be n - k(k+1)/2.

In this case, we want to find the letter at position 280.

By calculating the triangular numbers, we find that 21 * 22 / 2 is the largest triangular number less than or equal to 280.

So, k = 21. The position of the letter within the 21st group will be:

280 - 21 * 22 / 2

= 280 - 231

= 49.

Therefore, the 280th letter in this sequence is the letter at position 49 in the 21st group, which is the letter I.