Answer:
see explanation
Step-by-step explanation:
Given the sequence
1, 3, 6, 10, 15
(a)
This is the sequence of triangular numbers.
After the first term the pattern is
+ 2, + 3, + 4, + 5, ............
(b)
Using this pattern then
a₆ = a₅ + 6 = 15 + 6 = 21
a₇ = a₆ + 7 = 21 + 7 = 28
a₈ = a₇ + 8 = 28 + 8 = 36
(c)
The n th term formula for triangular numbers is
[tex]a_{n}[/tex] = [tex]\frac{1}{2}[/tex] n(n + 1)
(d)
Substitute n = 21 into the formula
a₂₁ = [tex]\frac{1}{2}[/tex] × 21 × 22 = 21 × 11 = 231
