Sparx 6: Item D
Bookwork code: H43 $\left[\begin{array}{l}\text { Calculator } \\ \text { not allowed }\end{array}\right.$
The terms in the sequence below are divided by $\frac{1}{2}$ each time, starting with $1 \frac{1}{3}$..
Mario thinks that because the terms are being divided, the sequence will eventually have a term that is less than 1.
a) Is Mario correct? Write a sentence to explain your answer:
b) Work out the $4^{\text {th }}$ term in the sequence.
Give your answer as a fraction in its lowest terms.
Answer
b) The 4th term in the sequence is \(\boxed{\frac{32}{3}}\).
Step 1 ：a) Mario is not correct. As the terms are divided by \(\frac{1}{2}\) each time, they actually become larger, not smaller. The sequence will never have a term that is less than 1.
Step 2 ：b) The 4th term in the sequence is \(\boxed{\frac{32}{3}}\).
