Answer:
see explanation
Step-by-step explanation:
(a)
Using the recursive rule and a₁ = 15 , then
a₂ = a₁ - 3 = 15 - 3 = 12
a₃ = a₂ - 3 = 12 - 3 = 9
a₄ = a₃ - 3 = 9 - 3 = 6
The sequence is 15, 12, 9, 6, ....
This is an arithmetic sequence with n th term ( explicit rule )
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 15 and d = - 3 , then
= 15 - 3(n - 1) = 15 - 3n + 3 = 18 - 3n
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(b)
Using the recursive rule and t₁ = 108 , then
t₂ = t₁ = × 108 = 36
t₃ = t₂ = × 36 = 12
t₄ = t₃ = × 12 = 4
The sequence is 108, 36, 12, 4, ......
This is a geometric sequence with n th term
= t₁
where t₁ is the first term and r the common ratio
Here t₁ = 108 and r = , then
= 108