For the following number sequence: \[\frac{1}{2}, \frac{3}{7}, \frac{5}{12}, \frac{7}{17}, \frac{9}{

Question

For the following number sequence: $$\frac{1}{2}, \frac{3}{7}, \frac{5}{12}, \frac{7}{17}, \frac{9}{22}, \dots$$ Write down the next two terms of the sequence. Find a formula for the $n^{th}$ term of the sequence in terms of $n$. Hence find the $16^{th}$ term. Find the lowest common multiple of the denominators of the $7^{th}$ and the $11^{th}$ term. Hence, find the difference between the $7^{th}$ and the $11^{th}$ term.

Accepted Answer

(i) $\frac{11}{27}$ and $\frac{13}{32}$ (ii) $T_n=\frac{2n-1}{5n-3}$ (iii) $\frac{31}{77}$ (iv) LCM $=416$ and difference $=\frac{1}{416}$

Number Patterns

Number Patterns

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