Sequence formulas

Today, we discussed how to define formulas (or rules) for sequences. This can be done with a recursive formula that defines each new term in the sequence by how to make it from the previous term. For example, the recursive formula for 5, 8, 11, 14, ... is:

• a₁ = 5 ← This is the starting or first term
• a_n = a_n-1 + 3 ← This is the what the sequence does, it adds 3 to the previous term.

This can also be done with an explicit formula which defines each new term in the sequence based on its position. For example, the explicit formula for 5, 8, 11, 14, ... is:

• First, we recognize that there is a rate of change of 3 for the terms in the sequence. This becomes the slope for the formula. We will start with a_n = 3n
• But, when we substitute n = 1 to find the first term, 3 * 1 = 3. This is 2 units short of the first term. We will add 2 to our formula to bring the output values up to the sequence terms.
• a_n = 3n + 2

Homework: Complete the handout with Sequences: Part 5 and Sequences Homework on the front and back. We will spend Monday reviewing all of the sequences concepts. We have a test scheduled for Wednesday. There will be a review session in the morning, Tuesday the 22nd, at 7:45 in room 4303.

Have a great weekend!

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