Question

The first term
of two A.P.s are equal and the ratios of their common

differences is
1:2. If the 7th term
of first AP and 21th term of
secon
second A.P. are 23 and 125 respe
- and 125 respectively. Find two A.P.S.​

Answer 1

Let the first term be a.

The common difference of two A. P are in the ratio 1 :2.

So let the common differences be d, 2d respectively.

7th term of first A. P

⇒ a + ( 7 - 1) d

⇒ a + 6d

Given, 7th term of first A. P = 23

⇒ a + 6d = 23 ____ ( Equation 1)

21th term of second A. P

⇒ a + ( 21 - 1) 2d

⇒ a + 40d

Given, 21th term of second A. P = 125

⇒ a + 40d = 125 ______ ( Equation 2)

Solving (1) & (2)

a + 40 d = 125

a + 6d = 23

Subtracting them gives,

⇒34d = 102

⇒ d = 3

Solving for a

⇒ a + 6(3) = 23

⇒ a = 23 - 18

⇒ a = 5

So, The first AP is

5, 8, 11, 14, 17, 20,......

So, The second AP is

5, 11, 17, 23, 29, 35,.......