Question

which term of the sequence 18,12,8........... is 512÷729?

Answer 1

6 is the sequence of term
hope it helps you

Answer 2

The answer is given below :

The given sequence is
18, 12, 8, ...

It is a Geometric Progression.

First term (a) = 18

Common difference (r) = 12/18 = 2/3

Let us consider that 512/729 be the n-th term of the sequence.

Then, a × r^(n - 1) = 512/729

⇒ 18 × (2^3)^(n - 1) = 512/729

⇒ 18 × (2/3)^n × (2/3)^(-1) = 512/729,
since x^(a + b) = x^a × x^b

⇒ 18 × 3/2 × (2/3)^n = 512/729,
since (2/3)^(-1) = 1/(2/3) = 3/2

⇒ 27 × (2/3)^n = 512/729

⇒ (2/3)^n = 512/729 × 1/27

⇒ (2/3)^n = 512/19683

⇒ (2/3)^n = (2/3)^9

Comparing the powers, we get n = 9

Therefore, the 9th term of the given sequence is 512/729.

Thank you for your question.