In a geometric progression ,the sum of 3rd and 4th term is 108. if the sum of the 4th and 5th term is 324, determine the: common ratio, first term and the 12th term.

see explanation

Step-by-step explanation:

The terms of a geometric progression are

a, ar, ar², ar³, ...... , a

Thus the sum of the third and fourth is

ar² + ar³ = 108 → (1)

The sum of the fourth and fifth is

ar³ + a = 324 → (2)

Factorise both equations

ar²(1 + r) = 108 → (3)

ar³(1 + r) = 324 → (4)

Divide (4) by (3)

=

Cancelling (1 + r) , a and r, gives

r = 3

Substitute r = 3 into (3) and solve for a

9a(4) = 108

36a = 108 ( divide both sides by 36 )

a = 3

The n th term is

= a with a = 3 and r = 3, hence

= 3 = 531441

1.true 2.false? ? i think. .

step-by-step explanation:

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497