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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 :

LammettHash

a) If the [tex]n[/tex]-th term is [tex]x_n = cn+d[/tex], then

[tex]x_1 = c + d = 16[/tex]

[tex]x_2 = 2c + d = 19[/tex]

Eliminating [tex]d[/tex],

[tex](2c+d) - (c+d) = 19-16 \implies c = 3[/tex]

Solving for [tex]d[/tex],

[tex]3 + d = 16 \implies d = 13[/tex]

Then

[tex]\boxed{x_n = 3n + 13}[/tex]

b) When [tex]n=11[/tex], we get

[tex]x_{11} = 3\cdot11 + 13 = \boxed{46}[/tex]

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