Question

the first term of two arithematic progression are equal and the ratips pf their commom difference is 1:2 if the 7th term of first a p and 21 st term of second arthematic progression are 23 and 125 find two arthematic progression
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Answer 1

LET THE FIRST TERM OF BOTH ARITHMETIC PROGRESSION BE a1 AND A1.

AND COMMON DIFFERENCE BE D1 AND D2.

ATQ

D1 / D2 = 1 / 2                                  

CONSIDER D1 = 1 AND D2 = 2.      

AND                                                  

a7 = 23 and A21 = 125                    

SUBSTITUTING D1 IN a7

a7 = 23

a + 6D1 = 23

a + 6 = 23

a = 17

AND

SUBSTITUTING D2 IN A21

A21 = 125    ⇒   A1 + 21D2 = 125    ⇒    A1 + 42 = 125   ⇒   A1 = 83