What is the tenth term of the sequence described by the following f1 = -2, tn =3tn-1

The 10th term will be:

t₁₀ = 39366

Step-by-step explanation:

Given the sequence

tₙ = -3 tₙ₋₁

Given

t₁ = -2

substitute n = 2, to determine the 2nd term

tₙ = -3 tₙ₋₁

t₂ = -3 tₙ₋₁

t₂ = -3 t₂₋₁

t₂ = -3 t₁

t₂ = -3 × -2        ∵ t₁ = -2

t₂ = 6

substitute n = 3, to determine the 3rd term

tₙ = -3 tₙ₋₁

t₃ = -3 t₃₋₁

t₃ = -3 t₂

t₃ = -3 × 6        ∵ t₂ = 6

t₃ = -18

substitute n = 4, to determine the 4th term

tₙ = -3 tₙ₋₁

t₄ = -3 t₄₋₁

t₄ = -3 t₃

t₄ = -3 × -18       ∵ t₃ = -18

t₄ = 54

substitute n = 5, to determine the 5th term

tₙ = -3 tₙ₋₁

t₅ = -3 t₅₋₁

t₅ = -3 t₄

t₅ = -3 × 54      ∵ t₄ = 54

t₅ = -162

substitute n = 6, to determine the 6th term

tₙ = -3 tₙ₋₁

t₆ = -3 t₆₋₁

t₆ = -3 t₅

t₆ = -3 × -162      ∵ t₅ = -162

t₆ = 486

substitute n = 7, to determine the 7th term

tₙ = -3 tₙ₋₁

t₇ = -3 t₇₋₁

t₇ = -3 t₆  

t₇ = -3 × 486      ∵ t₆ = 486

t₇ = -1458

substitute n = 8, to determine the 8th term

tₙ = -3 tₙ₋₁

t₈ = -3 t₈₋₁

t₈ = -3 t₇  

t₈ = -3 ×  -1458      ∵ t₇ = -1458

t₈ = 4374

substitute n = 9, to determine the 9th term

tₙ = -3 tₙ₋₁

t₉ = -3 t₉₋₁

t₉ = -3 t₈  

t₉ = -3 ×  4374      ∵ t₈ = 4374

t₉ = -13122

substitute n = 10, to determine the 10th term

tₙ = -3 tₙ₋₁

t₁₀ = -3 t₁₀₋₁

t₁₀ = -3 t₉  

t₁₀ = -3 × -13122     ∵ t₉ = -13122

t₁₀ = 39366

Therefore, the 10th term will be:

t₁₀ = 39366

b.an increase in a causes b to decrease

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