Question

if 6 time the 6th term of anA.P is equal to 9 time its 9th term,then show that its 15th term is zero.​

Answer 1

Step-by-step explanation:

6(a+5d)=9(a+8d)

or, 6a+30d=9a+72d

or, 3a+42d=0

or, a+12d=0

or, a=−12d

Now, a15=a+14d=−12d+14d=2d

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Answer 2

Step-by-step explanation:

6th term= a+5d

9th term = a+8d

6(6th term) = 9(9th term)

6(a+5d) = 9(a+8d)

6a+30d = 9a+72d

3a= -42d

a= -14d

15th term= a+14d

put a= -14d

15th term = -14d+14d= 0

hence 15th term= 0