Series Formulas
Geometric Series
- a = first term
- r = common ratio (found by )
- n = number of terms
- If r = 1, then
Finding r: Divide any term by the previous term. Check that ratio is consistent across all consecutive pairs.
Arithmetic Series
Alternative form:
- a = first term
- d = common difference
- n = number of terms
- t₁ = first term, tₙ = last term
Kahn acc
q1
Vince went on a 3 day hiking trip. Each day, he walked 3/4 the distance that he walked the day before. He walked 83.25 kilometers total in the trip.
a + a * 3/4 + a * 3/4 * 3/4 = 83.25
a + 3/4a + 9/16a = 83.25
1 + 3/4 + 9/16 = 37/16
37/16a = 83.25
a = 83.25/(37/16) = 36
a = 36
q2
A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers 5% more than the number of shoppers the day before. The total number of shoppers over the first 10 days is 1258.
sum = 1258
a + 1.05a + 1.05(1.05)a + … = 1258
How many shoppers were at the mall on the first day?