0 like 0 dislike
208 views

The sequence $4 ; 9 ; x ; 37 ; ...$ is a quadratic sequence.

1. Calculate $x$
2. Hence, or otherwise, determine the nth term of the sequence
| 208 views

0 like 0 dislike
1. 1st difference= 5,x-9,37-x,...

2nd difference= x-9-5, 37-x-(x-9),...

since 2nd difference is constant,

x-9-5 = 37-x-(x-9)

x-14=37-2x+9

3x= 60

x=20

2.  2a= x-9-5 = 20-9-5= 6

2a= 6

a= 3

3a+b=5

b= 5-3(3)

b= -4

a+b+c= 4

c= 4-3-(-4)

c= 5

Therefore nth term = 3n^2 -4n +5
by Silver Status (28.5k points)

0 like 0 dislike
{"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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://tedsf.org/qna/119/the-sequence-4-9-x-37-is-a-quadratic-sequence", "fetch_time": 1591507110000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2020-24/segments/1590348523564.99/warc/CC-MAIN-20200607044626-20200607074626-00562.warc.gz", "warc_record_offset": 533266756, "warc_record_length": 14003, "token_count": 246, "char_count": 534, "score": 3.78125, "int_score": 4, "crawl": "CC-MAIN-2020-24", "snapshot_type": "latest", "language": "en", "language_score": 0.7813537120819092, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00050-of-00064.parquet"}