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Big Ideas Math Integrated I, 2016

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Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 30 Page 319

Can you find the common difference just by looking at the explicit formula?

$a_{1} = - 2,$ $a_{n} = a_{n - 1} - 4$

Practice makes perfect

The explicit formula of an arithmetic sequence combines the information provided by the two equations of the recursive form into a single equation.

Explicit : Recursive : a_{n} = a_{1} + (n - 1) d; a_{1} = a_{1}, a_{n} = a_{n - 1} + d

In these formulas,

d

is the common difference and

a_{1}

is the first term. Looking at the given explicit formula, we can identify the common difference

d

as the coefficient of the

n -

term. Then we will calculate the value of the first term

a_{1} .

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Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320