Question

if 6times the 6th term of an A.P is equal to 9times the 9th term Find the 15th term

Answer 1

6.(a+5d)=9.(a+8d)
6a+30d=9a+72d
-3a=42d
a=-14d
15th term=a+14d
15th term=-14d+14d
15th term=0

Answer 2

Given,

6 times the 6th term of an AP = 9 times of its 9th term

To find,

The value of the 15th term.

Solution,

The 15th term of the AP will be 0.

According to the question,

6 times the 6th term of an AP = 9 times of its 9th term

6.a6 = 9.a9

[The formula to find the nth term is a+(n-1)d where a is the first term, n is the number of the term and d is the common difference.]

6[a+(n-1)d] = 9[a+(n-1)d]

6[a+(6-1)d] = 9[a+(9-1)d]

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

6a+30d = 9a+72d

Moving the terms with a on the left-hand side and with d on the right-hand side,

6a-9a = 72d-30d

-3a = 42d

a = -42d/3

a = -14d ---(1)

Now,

a15 = a+(n-1)d

a15 = a+(15-1)d

a15 = a+14d

Putting the value of a from equation 1,

a15 = -14d+14d

a15 = 0

Hence, the 15th term of the AP is 0.