2026 NASS P1 Q24

2026 NASS P1 Q24

Secondary 4
6 marks

The first four terms in a sequence of numbers, \(T_1,T_2,T_3,T_4,\ldots\) are given as shown.

\(\begin{aligned} T_1&=1+2+4=7 \\ T_2&=2+5+9=16 \\ T_3&=4+8+16=28 \\ T_4&=8+11+25=44 \end{aligned}\)

  1. Find an expression, in terms of \(n\), for the \(n\)th term, \(T_n\), of the sequence.[2]
  2. Show that \(T_n-T_{n-1}=2^{n-2}+2n+4\).[3]
  3. Hence, explain why the difference between consecutive terms in the sequence is always an even number.[1]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \(T_n=2^{n-1}+3n-1+(n+1)^2\). (b) \(2^{n-2}+2n+4\) (shown). (c) Even for \(n\geq3\); the first difference is 9, so “always” is false as printed.

Need help? Join our JC Math tuition classes.

Learn more