Final Study Guide

Question 1

What is the formula for the common difference in an arithmetic sequence?

Answer 1

d = (a_n+1)-a_n

Question 2

What is the general term of an arithmetic sequence?

Answer 2

a_n= a_1+ (n-1)d

Question 3

How do you calculate the sum of the first n terms in an arithmetic sequence?

Answer 3

Sn = n/2 * (a1 + an)

Question 4

What is another formula for the sum of the first n terms in an arithmetic sequence?

Answer 4

Sn = n/2 * (2a1 + (n-1)d)

Question 5

What is the common ratio in a geometric sequence?

Answer 5

r = (a_n+1)/a_n

Question 6

What is the general term of a geometric sequence?

Answer 6

An = a1 * r^(n-1)

Question 7

How do you calculate the sum of the first n terms in a geometric sequence?

Answer 7

Sn = a1 * (1 - r^n) / (1 - r)

Question 8

What is the formula for the sum of the terms of an infinite geometric sequence?

Answer 8

S∞ = a1 / (1 - r)

Question 9

Binomial Coefficient nCr

Answer 9

n!/((r!)(n-r)!) where r is smaller than or equal to n

Question 10

Future Value of an Ordinary Annuity

Answer 10

S = R[((1+i)^n-1)/i)] where R is the payment at the end of each period, I is the interest rate per period, and n is the number of periods

Question 11

Compound Interest

Answer 11

A = P(1+r/n)^nt where P is the principal, r is the annual interest rate, n is the number of compounds per year, and t is the time in years

Question 12

Continuous Compound Interest

Answer 12

A = Pe^(rt) where P is the principal, r is the annual interest rate, and t is the time in years