iGCSE Mathematics (0580) - C2.7 Sequences- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
(a)
Substitute $n = 1, 2, 3$ into the formula:
$1^2 – 4 = 1 – 4 = -3$
$2^2 – 4 = 4 – 4 = 0$
$3^2 – 4 = 9 – 4 = 5$
✅ Answer: $-3, 0, 5$
(b)
Find the common difference between consecutive terms: $2 – 5 = -3$. This means it starts with $-3n$.
To find the constant, look at the $0^{\text{th}}$ term (or subtract the difference from the first term): $5 – (-3) = 8$.
The general rule is $-3n + 8$.
✅ Answer: $-3n + 8$
▶️ Answer/Explanation
(a)
To get from the $1$st term ($2$) to the $4$th term ($20$), you add $k$ three times ($2 + 3k = 20$).
Solving for $k$: $3k = 18 \Rightarrow k = 6$.
Now, just add $6$ to find $e$ and $f$: $e = 2 + 6 = 8$, and $f = 8 + 6 = 14$.
✅ Answer: $e = 8$, $f = 14$, $k = 6$
(b)
The sequence drops by $2$ each time, so the rule includes $-2n$.
The “zeroth” term (the term before $9$) would be $9 + 2 = 11$.
Combining these gives the formula $11 – 2n$.
✅ Answer: $11 – 2n$