pre calc

Question 1

arithmetic sum formula

Answer 1

sn = n(a1 + an)/2)

Question 2

geometric sum formula

Answer 2

sn= a1 (1- r^ n) / ( 1 - r )

Question 3

recursive geometric

Answer 3

an = a(n-1) x r

Question 4

recursive arithmetic

Answer 4

an = a(n-1) + d

Question 5

explicit arithmetic

Answer 5

an = a1+ d(n-1)

Question 6

explicit arithmetic

Answer 6

an = a0 + dn

Question 7

explicit geometric

Answer 7

an = a1 x r ^ (n-1)
an = a0 x r^n

Question 8

how to find the 0th term

Answer 8

a0 = a1/ r

Question 9

s infinity equation geometric

Answer 9

s(infinity) = a1/ 1-r

Question 10

proof by induction

Answer 10

1. base case show that it works for n = 1 and it equals each other
2. hypothesis: assume that it works for n = k; so that it equals each other
3. show that sk+1 = sk plus ak+1
4. if it works then by induction it works

Question 11

continuous compound formula

Answer 11

A = P(e) ^ rt

Question 12

compound formula

Answer 12

A = P ( 1 + r/n) ^ nt

r = rate
n = number of times compounding yearly
t = number of years
P = initial value

so if monthly then 12 would be n

Question 13

half life formula

Answer 13

A = P (1/2) ^ x/T

x = time
T = half life

percentage is A/P

Question 14

what are the three log properties

Answer 14

logb (a) + logb (c) = logb (a * c)

logb (a) -logb (c) = logb (a/c)

logb (a) ^ c = C logb (a)

Question 15

how do logs work

Answer 15

logb (a) = x ——> a = b^x