Question

The start of an arithmetic sequence is

16, 19, 22, 25, ...
The rule for the sequence can be written in the
form xn = cn +d, where c and d are
numbers.
a) By first calculating the values of c and d,
work out the rule for the sequence.
b) What is the value of x11?

Answer 1

a) If the
`n`-th term is
`x_n = cn+d`, then

`x_1 = c + d = 16`

`x_2 = 2c + d = 19`

Eliminating
`d`,

`(2c+d) - (c+d) = 19-16 \implies c = 3`

Solving for
`d`,

`3 + d = 16 \implies d = 13`

Then

`\boxed{x_n = 3n + 13}`

b) When
`n=11`, we get

`x_(11) = 3\cdot11 + 13 = \boxed{46}`