Question

The first term of two a.ps are equal andthe ratios of their common difference is 1:2. if the 7th term of the first a.p and 21st term od second a.p are 23 and 125 respectively. find the two a.ps

Answer 1

$\large\bf\underline{Given:-}$

The first term of two aps are equal and the ratios of their common difference is 1:2

If the 7th term of first ap and 21th term of second ap are 23 and 125 respectively. find two aps.

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$\large\bf\underline{According to question we have:-}$

★ So a7 = 23

★ Now a + 6d = 23 Or a = 23 – 6d ........( 1 )

★Also a21 = 125

★Now a + 20b = 125.........( 2 )

★ Or 23 – 6d + 20 b = 125 (from 1)

• 20 b – 6d = 102
• 10 b – 3d = 51

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$\large\bf\underline{Solution:-}$ 

Now according to question d/b = 1/2  

• Now d = 1x and b = 2x (for some positive value x)
• Now 10 b – 3d = 51
• 10(2x) – 3 (x) = 51
• 17 x = 51
• Or x = 3
• Therefore d = 3, b = 6
• Put d = 3 in equation 1 we get
• So a + 6(3) = 23
• Or a = 23 – 18
• Or a = 5

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$\large\bf\underline{Answer:-}$

• Therefore first A.P is 5,8,11 
• Second A.P is 5,11,17

Answer 2

Step-by-step explanation:

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