ಒಂದು ಸಮಾಂತರ ಶ್ರೇಢಿಯ ಮೊದಲ 4 ಪದಗಳ ಮೊತ್ತ 40, ಒಂದು ಮತ್ತು ಮೂರನೇ ಪದಗಳ ಮೊತ್ತ ಮತ್ತು ಎರಡು ಮತ್ತು ನಾಲ್ಕನೇ ಪದಗಳ ಮೊತ್ತಗಳ ಅನುಪಾತ 2:3 ಅದರೆ ಶ್ರೇಣಿಯ ನಾಲ್ಕ ಪದಗಳನ್ನು ಕಂಡುಹಿಡಿಯಿರಿ
Answers
Given : an AP , Sum of first four terms is 40.
Ratio of sum of 1st and term term to sum of 2nd and 4th term is 2:3
To Find : AP
Solution:
Let say AP is
a , a + d , a + 2d , a + 3d , ________
a + a + d + a + 2d + a + 3d = 40
=> 4a + 6d = 40
=> 2a + 3d = 20
(a + a + 2d) : ( a + d + a + 3d) = 2 : 3
=> (2a + 2d ) : ( 2a + 4d ) = 2 : 3
=> (a + d) : (a + 2d) = 2 : 3
=> 3(a + d) = 2(a + 2d)
=> 3a + 3d = 2a + 4d
=> a = d
2a + 3d = 20
=> 2a + 3a = 20
=> a = 4
d = 4
AP is
4 , 8 , 12 , 16
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