{"status": "success", "data": {"description_md": "A sequence $a_n$ has $a_1=12$, $a_2=24$, and $a_3=48$.\n\nWhen Harry sees the first three terms of this sequence, he thinks:\n\n*\"This is a geometric sequence!\"*\n\nHowever, when Larry (who is in a concerning and steadily declining mental state of being) sees the first three terms, he instead thinks:\n\n*\"Wow! This sequence is the result of adding together the respective terms of an arithmetic sequence with nonzero difference and a geometric sequence with a positive ratio!\"*\n\nBased on their respective thoughts, Harry and Larry form their own version of the sequence $a_n$. Find the positive difference between Harry's value of $a_5$ and Larry's value of $a_5$.", "description_html": "

A sequence a_n has a_1=12, a_2=24, and a_3=48.

When Harry sees the first three terms of this sequence, he thinks:

“This is a geometric sequence!”

However, when Larry (who is in a concerning and steadily declining mental state of being) sees the first three terms, he instead thinks:

“Wow! This sequence is the result of adding together the respective terms of an arithmetic sequence with nonzero difference and a geometric sequence with a positive ratio!”

Based on their respective thoughts, Harry and Larry form their own version of the sequence a_n. Find the positive difference between Harry’s value of a_5 and Larry’s value of a_5.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Christmas Contest - Team Round - Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p25", "prev": "/problem/christmas1_team-p23"}}