Question

Please help..............

Answer 1

see explanation

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

`a_(n)` =
`(1)/(2)` n(n + 1)

(d)

Substitute n = 21 into the formula

a₂₁ =
`(1)/(2)` × 21 × 22 = 21 × 11 = 231