Question

3. The sequence 8, 32, 128, 512, … represents the number of sit-ups Billy did during each workout session, starting with his first week of exercising.
(a) What is the recursive rule for the sequence?
(b) What is the iterative rule for the sequence?

Answer 1

The given sequence the recursive function will be $a_n = 4a_{n-1}$

The iterative rule for the sequence is $T_n = 8(4)^{n-1$

Sequence and series

Given the sequence of numbers  8, 32, 128, 512, …

• a1 = 8
• a2 = 32 = 4(8)
• a3 = 128 = 4(32)

From the given sequence the recursive function will be $a_n = 4a_{n-1}$

For the iterative sequence, we will use the common ratio and the first term as shown;

$T_n=ar^{n-1}\\T_n=8(4)^{n-1}$

Hence the iterative rule for the sequence is $T_n = 8(4)^{n-1$

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