5.4.3 Sum of the First n Terms of a Geometric Progression

5.4.3 Sum of the First n Terms of Geometric Progressions

(F) Sum of the First n Terms of Geometric Progressions

\begin{array}{l} S_{n} = \frac{a (r^{n} - 1)}{r - 1}, r > 1 \\ S_{n} = \frac{a (1 - r^{n})}{1 - r}, r < 1 \end{array}

a = first term

r = common ratio

n = number of term

S_n = sum of the first n terms

Example 1:

Find the sum of each of the following geometric progressions.

(a) 1, 2, 4, … up to the first 7 terms

(b) 9, 3, 1, ⅓, … up to the first 6 terms
(c) 12, 3, ….,

\frac{3}{64}

[Smart TIPS: You can find n if you know the last term]

Solution: