1. Calculate the production in year 8. Calculate the total production
STARTER
The production on a wheat farm is decreasing due to the increase in the salinity in the soil. In year 1 the production was 660 tonnes. In year 2 the production was tonnes and in year 3 the production was tonnes.
Calculate the production in
year 8.
Calculate the total production
for years 1-10.
660 x (0.92)7 = tonnes
660 x ( ) = 4666 tonnes
(1 – 0.92)

2. Note 9: Sum to Infinity
When a geometric sequence has a common ratio between –1 and 1, then the terms become smaller
The sum to infinity of a geometric sequence is the number that the sum of all terms gets very close to but never actually reaches

3. Discussion:
<24, 12, 6, 3, 1.5, 0.75, 0.375, …>
If we add the terms in succession (called taking partial sums) we get 24, 36, 42, 45, 46.5, 47.25, , etc.
This gets closer and closer to 48 without ever reaching 48 exactly. So the sum to infinity of this sequence is 48

4. The sum to infinity of geometric terms is: S∞ = a 1 - r
Example: Find the sum to infinity for the sequence
12, -3, 3/4, -3/16, …
a =12 r = -3/12 = -1/4
S∞ = 12
1 - -1/4
for -1 < r < 1 only
= 9.6

5. Sensible Selection
Page 117
Exercise 14.3 – 14.4