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?