Question

ಎರಡು ಸಮಾಂತರ ಶ್ರೇಢಿಯ ಮೊದಲ ಪದಗಳು ಸಮನಾಗಿದ್ದು, ಸಾಮಾನ್ಯ ವ್ಯತ್ಯಾಸಗಳ
ಅನುಪಾತ 1 : 2 ಆಗಿದೆ. ಮೊದಲನೇ ಸಮಾಂತರ ಶ್ರೇಢಿಯ 7ನೇ ಪದ ಹಾಗೂ ಎರಡನೇ
ಸಮಾಂತರ ಶ್ರೇಢಿಯ 21ನೇ ಪದ ಕ್ರಮವಾಗಿ 23 ಮತ್ತು 125 ಆದರೆ, ಎರಡು ಸಮಾಂತರ
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2 |
- 10
ಶ್ರೇಢಿಗಳನ್ನು ಕಂಡುಹಿಡಿಯಿರಿ.
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01​

Answer 1

SOLUTION

GIVEN

The first term of two A.P.s are equal and the ratios of their common differences is 1 : 2

The 7th term of first term A.P. and 21th term of second A.P. are 23 and 125 respectively .

TO DETERMINE

The two AP

FORMULA TO BE IMPLEMENTED

In an arithmetic progression

First term = a

Common Difference = d

Then n th term = a + ( n - 1 )d

EVALUATION

Here it is given that the first term of two A.P.s are equal and the ratios of their common differences is 1 : 2

Let first term of both AP = a

Common Difference of first AP = d

Common Difference of second AP = 2d

Now 7 th term of first AP

= a + 6d

∴ a + 6d = 23 - - - - - (1)

Again 21 th term of second AP

= a + ( 20 × 2d )

= a + 40d

∴ a + 40d = 125 - - - - - (2)

Equation 2 - Equation 1 gives

34d = 102

⇒ d = 3

From Equation 1 we get

a = 23 - 6d = 23 - 18 = 5

∴ First term of both AP = 5

So Common Difference of first AP = 3

Common Difference of second AP = 6

So the required

First AP : 5 , 8 , 11 , 14 ,...

Second AP : 5 , 11 , 17 , 23 ,....

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