Question

Find the G.P. whose 5th and 8th terms are 80 and 640 respectively.

Answer 1

Let the first term be a and the common ratio be r. Then,

$$T_5 = ar^4 = 80 \quad ...(i)$$

$$T_8 = ar^7 = 640 \quad ...(ii)$$

Dividing (ii) by (i):

$$r^3 = \frac{640}{80} = 8$$

$$\Rightarrow r = 2$$

Putting $$r = 2$$ in (i):

$$a \times 2^4 = 80$$

$$\Rightarrow a \times 16 = 80$$

$$\Rightarrow a = 5$$

So the G.P. is 5, 10, 20, 40, 80, 160, 320, 640, ... with a = 5 and r = 2.