The formula for obtaining the value of a term of a sequence is given as a
as a recursive formula.
Responses:
- The information as a sequence is; R1, 2·R1, 4·R1, 8·R1, 16·R1, ...
- The sequence of the information is a geometric sequence
How is the given information expressed as a sequence?
The amount of pocket money Smith gets = 2 × The amount he gets in the previous day
The amount Smith gets on the first day = R1
Required:
The given information expressed as a sequence.
Solution:
The amount of money smith gets can be expressed as follows;
Amount he gets on day 1 = R1
On day 2, R2 = 2·R1
On day 3, R3 = 2·R2 = 2·2·R1 = 4·R1
On day 4, R4 = 2·R3 = 2·2·2·R1 = 8·R1
On day 5, R5 = 2·R4 = 2·2·2·2··R1 = 16·R1
The information written as a sequence is therefore;
- R1, 2·R1, 4·R1, 8·R1, 16·R1, ...
- The type of sequence is a geometric sequence, or progression where the first term is R1, and the common ratio, r = 2
Learn more about geometric sequence here:
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