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Home10th Class

SSLC Mathematics: Arithmetic Progression - Important Formulas

byEnglish Hub
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SSLC Mathematics: Arithmetic Progression - Important Formulas

ಹತ್ತನೇ ತರಗತಿ ಕನ್ನಡ ಮಾಧ್ಯಮದ ವಿದ್ಯಾರ್ಥಿಗಳಿಗಾಗಿ ಸಮಾಂತರ ಶ್ರೇಢಿಗಳಿಗೆ ಸಂಬಂಧಿಸಿದ Important Formula ಗಳನ್ನು ಇಲ್ಲಿ ಅಳವಡಿಸಲಾಗಿದೆ.

ವಿದ್ಯಾರ್ಥಿಗಳು ಸತತವಾಗಿ ಇವುಗಳನ್ನು ಪ್ರತಿದಿನ ಅಭ್ಯಾಸ ಮಾಡಿದರೆ ಗಣಿತ ವಿಷಯದಲ್ಲಿ ಸಮಾಂತರ ಶ್ರೇಢಿಗಳಿಗೆ ಸಂಬಂಧಿಸಿದ ಪ್ರಶ್ನೆಗಳನ್ನು ಪರೀಕ್ಷೆಯಲ್ಲಿ ಅತ್ಯಂತ ಸರಳವಾಗಿ ಬಿಡಿಸಬಹುದಾಗಿದೆ.

1. ಸಮಾಂತರ ಶ್ರೇಢಿಗಳು

ಸಮಾಂತರ ಶ್ರೇಢಿಯ ವ್ಯಾಖ್ಯೆ

 ಮೊದಲ ಪದವನ್ನು ಹೊರತುಪಡಿಸಿ ಪ್ರತಿಯೊಂದು ಪದವನ್ನು ಪಡೆಯಲು ಅದರ ಹಿಂದಿನ ಪದಕ್ಕೆ ಒಂದು ನಿರ್ದಿಷ್ಟ ಸಂಖ್ಯೆಯನ್ನು ಕೂಡಿಸುವುದರಿಂದ ಪಡೆಯುವ ಸಂಖ್ಯಾ ಪಟ್ಟಿಯೇ ಸಮಾಂತರ ಶ್ರೇಢಿ
ಉದಾಹರಣೆ:
  4,7,10,13,16,19,22.
  2,4,6,8,10...

ಸಮಾಂತರ ಶ್ರೇಢಿಯ ಸಾಮಾನ್ಯ ರೂಪ

a, a+d, a+2d,a+3d...
a → ಮೊದಲ ಪದ
d → ಸಾಮಾನ್ಯ ವ್ಯತ್ಯಾಸ

ಸಮಾಂತರ ಶ್ರೇಢಿಯ ವಿಧಗಳು

1) ಪರಿಮಿತ ಸಮಾಂತರ ಶ್ರೇಢಿ
 ಉದಾಹರಣೆ: 3,6,9,12,15...24
2) ಅಪರಿಮಿತ ಸಮಾಂತರ ಶ್ರೇಢಿ
 ಉದಾಹರಣೆ: 3,6,9,12,15...

ಸಮಾಂತರ ಶ್ರೇಢಿಯ ಸೂತ್ರಗಳು

ಸಮಾಂತರ ಶ್ರೇಢಿಯ nನೇ ಪದ an = a+(n-1)d
ಮೊದಲ n ಪದಗಳ ಮೊತ್ತ Sn =
n / 2
[2a+(n-1)d]
ಮೊದಲ n ಪದಗಳ ಮೊತ್ತ Sn =
n / 2
[a+l]
ಮೊದಲ n ಸ್ವಾಭಾವಿಕ ಸಂಖ್ಯೆಗಳ ಮೊತ್ತ Sn =
n(n+1) / 2
ಸಮಾಂತರ ಶ್ರೇಢಿಯ nನೇ ಪದ an = Sn - Sn-1
ಸಾಮಾನ್ಯ ವ್ಯತ್ಯಾಸ d = an - an-1
3 ಅನುಕ್ರಮ ಪದಗಳು (a-d), a, (a+d)
4 ಅನುಕ್ರಮ ಪದಗಳು (a-3d), (a-d), (a+d), (a+3d)

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