Question

the sum of 5th and 9th term of an AP is 30. if it's 25th term is 3 times its 18th term . find the AP

Answer 1

Heya !!


Let a be the first term and D be the common difference.



Then,


5th term = A+4D


And,


9th term = A + 8D



According to the question,


5th term + 9th term = 30



A + 4D + A + 8D = 30



2A + 12D = 30



A + 6D = 15 ---------(1)



And,


25th term= 3 ( 18th term )



A + 24D = 3 ( A + 17D )



A + 24D = 3A + 51D




3A - A = 24D - 51D


2A = - 27D



A = (-27D/2)



Putting the Value of A in equation (1)



A + 6D = 15


-27D/2 + 6D = 15




-27D + 12D = 30




-15D = 30



D = -30 / 15 = -2



Putting the Value of D in ,


A = -27D/2 = -27 × -2 / 2





A = 27





Therefore,



First term ( A ) = 27


And,



Common difference ( D ) = -2




So,



Second term = A + D = 27-2 = 25




Third term = A + 2D = 27 + 2 × -2 = 23


AP = 27 , 25 , 23 , 21. ........

Answer 2

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