Question

Calculate the 8th term of the G.P. 9, 3, 1, ...

Answer 1

Answer:

The 8th term of the G.P. 9, 3, 1, ... is $\frac{1}{243}$.

Step-by-step explanation:

Let x and y ≠ 0 be real numbers. Then the number of forms x, xy, xy², xy³, ...... is called a Geometric Progression (G.P). The number 'x' is called the first term and the number 'y' is called the common ratio.

Step 1:- To find the 8th term we need to use the $n^{th}$ term formula,

⇒ tₙ = $xy^{n-1}$

Step 2:- According to the formula,

first term 'x' = 9

common ratio 'y' = $y=\frac{t_{2}}{t_{1}}$  [according to the formula common ratio 'y' = t₂ ÷t₁]

⇒ y = $\frac{3}{9}$,

⇒ y = $\frac{1}{3}$,

Step 3:- Now, t₈ = $9 \times\left(\frac{1}{3}\right)^{8-1}$ [Here, a = 9, y = $\frac{1}{3}$, and n = 8, as given above]

⇒ t₈ = $9 \times\left(\frac{1}{3}\right)^{7}$,

⇒ t₈ = $\frac{1}{243}$.

∴The 8th term of GP 9,3,1,..... is $\frac{1}{243}$.

To know more about G.P and its different questions,

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