Question

Find the sum of the first 9 terms in the following geometric series. 64+32+16+

Answer 1

Answer:

The sum of the first 9 terms in the geometric series is 127.75

Step-by-step explanation:

In the geometric series, there is a constant ratio between each two consecutive numbers

Examples:

5,  10,  20,  40,  80,  ………………………. (×2)

5000,  1000,  200,  40,  …………………………(÷5)

General term (nth term) of a Geometric series is

a1 = a, a2 = ar, a3 = ar²,  a4 = ar³, ..........

$an=ar^{n-1}$, where

a is the first term

r is the constant ratio between each two consecutive terms

The sum of the first n terms of a Geometric series is calculated by this rule

$Sn=\frac{a(1-r^{n})}{1-r}$

Let us solve the question

∵ The geometric series is 64, 32, 16, .......................

∴ a = 64

∴ r = 32 ÷ 64 = 0.5

→ We need to find the sum of the first 9 terms

∴ n = 9

→ Substitute these values on the formula of the sum above

∴ $S9=\frac{64(1-0.5^{9})}{1-0.5}$

→ use the calculator to find the answer

∴ S9 = 127.75

 ∴ The sum of the first 9 terms in the geometric series is 127.75