# Thread:

1. ## Induction for sequences

OK, I am completely stupid when it comes to induction. Any help? I shouldn't have taken this class.

2. Use Mathematicla induction for part 1.
let $S_n$be a statement that $a_n$ is odd

Assume $S_{k-2}$ and $S_{k-1}$ are true and then prove $S_k$is true.

$a_k = 2a_{k-2} +3a_{k-1}$

Now $2a_{k-2}$ is even and $3a_{k-1}$ is odd since odd multiplied by odd is odd.

Sum of an even number and odd number is always odd.
so $a_k$is odd.
Hence $S_k$ is proved true.

base case $a_1$ and $a_2$are already give odd.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9302178025245667, "perplexity_flag": "middle"}