Exam-Style Questions.

1.	GCSE Higher

(a) The \(n\)th term of a sequence is \(2^n+2^{n+1}\)

Work out the 8th term of the sequence.

(b) The \(n\)th term of a different sequence is \(9(3^n + 3^{n+1})\)

Expand and express this expression as the sum of two powers of three.

Worked Solution

---

2.	IB Applications and Interpretation

In an old science fiction book the author described the intensity of reverse polarity, \(P\) measured in treckons, is a function of the nebula thrust, \(N\) measures in whovians. The intensity level is given by the following formula.

$$P = 7 \log_{10}(N \times 10^{8}), N \ge 0$$

(a) An space shuttle has a nebula thrust of \(9.1 × 10^{-3}\) whovians. Calculate the intensity level, \(P\) of the shuttle.

(b) A different space shuttle has an intensity level of 112 trekons. Find its nebula thrust, \(N\).

Worked Solution

---

3.	IB Analysis and Approaches

The following is an arithmetic sequence: \( \log_7 8 \text{, } \log_7 a \text{, } \log_7 b \text{, } \log_7 64 \) where \(a \gt 1 \text{ and } b \gt 1\)

(a) Show that 8, \(a\), \(b\), and 64 are four consecutive terms of a geometric sequence.

(b) Find the values of \(a\) and \(b\)

Worked Solution

---