30:00
1 of 5
Higher
Non-calculator
A24 Special sequences
Question 1 · 5 marks
Spec and skills
Paper scope: Paper 1: non-calculator practice
Spec A24
Spec A23
Spec A6
Original practice question
Answer and supported method checks
The
n
n
n
th triangular number is
T
n
=
n
(
n
+
1
)
2
T_n = \dfrac{n(n + 1)}{2}
T
n
=
2
n
(
n
+
1
)
.
(a)
Show that the sum of two consecutive triangular numbers,
T
n
+
T
n
+
1
T_n + T_{n + 1}
T
n
+
T
n
+
1
,
is always a square number.
3 marks
Write both triangular numbers.
T
n
+
T
n
+
1
=
T_n + T_{n+1} =
T
n
+
T
n
+
1
=
n
xⁿ
a/b
√
π
(
)