Question

Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10: 0.15, 0.015, 0.0015, ... 20 terms.

Answer 1

The given G.P. is 0.15, 0.015, 0.00015, …

Here, a = 0.15 and r = \(\frac{0.015}{0.15}\) = 0.1

Sn = a\(\frac{(1-rn)}{1-r}\)

∴ S20 = 0.15 \(\frac{[1-(0.1)20]}{1-0.1}\)

= \(\frac{0.15}{0.9}[{1-(0.1)20]}\)

= \(\frac{15}{90}{[1-(0.1)20]}\)

= \(\frac{1}{6}{[1-(0.1)20]}\)