Question

Show that the progression 0.4, 0.8, 1.6, ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 7th term.

Answer 1

To show it is a G.P.

$$\frac{0.8}{0.4} = 2, \frac{1.6}{0.8} = 2$$

Both ratios are the same (constant = 2), so the given numbers form a G.P.

(i) First term: $$a = 0.4$$

(ii) Common ratio: $$r = 2$$

(iii) nth term: $$T_n = ar^{n - 1} = 0.4 \times 2^{n - 1}$$

(iv) 7th term: $$T_7 = 0.4 \times 2^{(7 - 1)}$$

$$= 0.4 \times 2^6$$

$$= 0.4 \times 64$$

$$= 25.6$$

So, the 7th term is 25.6.