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# The fifth term in the progression $$9,27,81,{\dots}$$ is

### Question

The fifth term in the progression $$9,27,81,{\dots}$$ is

### Options

A) $$243$$

B) $$3^7$$

C) $$729$$

D) $$3^8$$

### Explanation:

If $$\cfrac{T_2}{T_1} = \cfrac{T_3}{T_2}$$, the progression is a G.P.
If $$T_2 - T_1 = T_3 - T_2$$, the progression is an A.P
Sine $$\frac{27}{9} = \frac{81}{27}$$, the progression is a G.P.
$$r = \cfrac{27}{9} = 3$$
$$T_5 = ar^{n-1}$$
$$= 9 \times 3^{5-1}$$
$$= 3^2 \times 3^4$$
$$T_5 = 3^6$$

## Dicussion (1)

• If $$\cfrac{T_2}{T_1} = \cfrac{T_3}{T_2}$$, the progression is a G.P.
If $$T_2 - T_1 = T_3 - T_2$$, the progression is an A.P
Sine $$\frac{27}{9} = \frac{81}{27}$$, the progression is a G.P.
$$r = \cfrac{27}{9} = 3$$
$$T_5 = ar^{n-1}$$
$$= 9 \times 3^{5-1}$$
$$= 3^2 \times 3^4$$
$$T_5 = 3^6$$