Question

1) If 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P. What is 13 times
the 13th term of this A.P.
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Answer 1

Answer:

13 times the 13th term is 0.

Step-by-step explanation:

The nth term of an AP is: $T_{n}=a+(n-1)d$

Here, a = first term, d = common difference.

It is provided that 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P.

The 4th and 9th term are:

$T_{4}=a+3d\\T_{9}=a+8d$

Determine the relation between a and d as follows:

$4(a+3d)=9(a+8d)\\4a+12d=9a+72d\\-5a=60d\\a=-12d$

Compute the 13th term as follows:

$T_{13}=a+(13-1)d\\=-12d+12d\\=0$

Thus, 13 times the 13th term is 0.

Answer 2

Answer:

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