Question

Which term of the geometric sequence 1/3,1/9,1/27......is 1/729

Answer 1

It is the 6th term in this geometric sequence as the common ratio is 1/3.

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Answer 2

Answer:

The 6th term in the geometric sequence 1/3, 1/9, 1/27, ..... is 1/729.

Step-by-step explanation:

Given,

The geometric sequence:

1/3, 1/9, 1/27, .....

To find,

In which term does the given geometric sequence contain 1/729?

Concept,

aₙ = a(r)ⁿ ⁻ ¹...(1)

where aₙ = nth term of G.P

           n = number of terms in the G.P

           a = first term in the G.P

           r = common ratio

Calculation,

Now, aₙ = 1/729, a = 1/3, and r = $\frac{\frac{1}{9} }{\frac{1}{3} }$ = 1/3, n = n substituting in equation (1) we get:

(1/729) = (1/3)(1/3)ⁿ ⁻ ¹

⇒ (1/729) = (1/3)ⁿ

⇒ 3ⁿ = 729

⇒ 3⁶ = 729

⇒ n = 6

Therefore, the 6th term in the geometric sequence 1/3, 1/9, 1/27, ..... is 1/729.

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