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 607.2 tonnes and in year 3 the production was 558.624 tonnes. Calculate the production in year 8. Calculate the total production for years 1-10. 660 x (0.92)7 = 368.179 tonnes 660 x (1- 0.9210) = 4666 tonnes (1 – 0.92)

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

Discussion: <24, 12, 6, 3, 1.5, 0.75, 0.375, 0.1875…> If we add the terms in succession (called taking partial sums) we get 24, 36, 42, 45, 46.5, 47.25, 47.625, 47.8125 etc. This gets closer and closer to 48 without ever reaching 48 exactly. So the sum to infinity of this sequence is 48

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

Sensible Selection Page 117 Exercise 14.3 – 14.4