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 term A.P. and 21th term of second A.P. are 23 and 125 respectively . find two A.P.s​

Answer 1

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.

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  

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

Therefore first A.P is 5,8,11-------and  

Second A.P is 5,11,17

Answer 2

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