A1: Lesson 10.1: Arithmetic Sequence

​Given the following sequence:

4, 7, 9, 12, ...

Is there a arithmetic pattern?

​

​

Sometimes...there is NO pattern.

​Finding specific terms from an arithmetic sequence:

formula: a_n = d(n - 1) + a¹

a₁: first term in the sequence

d: common difference

n: the term location you want to calculate

Example:

Given: -1, -4, -7, -10, ...

a₁ = -1 and d = -3​

​

Formula: ​a₁=-3n+2

​

Replace the n for the desired term needing to calculate.​

​Working With Scenarios:

You visit the Grand Canyon and drop a penny off the edge of the cliff. The Distance the penny will fall is 16 feet for the first second, 48 feet feet the next second, 80 feet the third second, and so on.

​

First: Record this sequence:

16,48,80,...​

​

​Next: Write an equation:

​ a₁ = 16 and d = 32

a_n = 32n - 16​

​

Predict the distance a penny falls at six seconds: 176 feet