Notes: `5, 13, 21, 29, 37, 45...` Decide whether the sequence can be represented perfectly by a linear or a quadratic model. If so, then find the model.

Thursday, April 15, 2010

The given sequence is:

$\displaystyle{5},{13},{21},{29},{37},{45}$

To determine if it is a linear sequence, take the difference between the consecutive terms.

$\displaystyle{5},{13},{21},{29},{37},{45}$

$\displaystyle\bigvee$ $\displaystyle\bigvee$ $\displaystyle\bigvee$ $\displaystyle\bigvee$ $\displaystyle\bigvee$

$\displaystyle{8}$ $\displaystyle{8}$ $\displaystyle{8}$ $\displaystyle{8}$ $\displaystyle{8}$

Since the difference between consecutive terms are the same, the given sequence is linear.

To determine the model of a linear sequence, apply the formula

$\displaystyle{a}_{{n}}={a}_{{1}}+{\left({n}-{1}\right)}{d}$

where an is the nth term, a1 is the first term, d is the common difference, and n is any positive integer.

Plugging in the values of a1 and d, the formula becomes:

$\displaystyle{a}_{{n}}={5}+{\left({n}-{1}\right)}{8}$

$\displaystyle{a}_{{n}}={5}+{8}{n}-{8}$

$\displaystyle{a}_{{n}}={8}{n}-{3}$

Therefore, the given sequence can be represented by a linear model which is $\displaystyle{a}_{{n}}={8}{n}-{3}$ .

Notes