If a 1 =6 and a n =-2a n-1 a 5 then find the value of a5

a₅ = 96

Step-by-step explanation:

We know that:

a₁ = 6

aₙ = -2*aₙ₋₁

Then we want to find the value of a₅

We can do it in two ways, we can use the relation to find the terms as:

a₂ = -2*a₁ = -2*6 = -12

a₃ = -2*a₂ = -2*(-12) = 24

a₄ = -2*a₃ = -2*24 = -48

a₅ = -2*a₄ = -2*(-48) = 96

Then we have a₅ = 96

And we know that this is a geometric sequence, where the ratio between terms is -2, then the n-th term can be written as:

aₙ = a₁*r^(n - 1)

where r is the ratio, in this case, r = -2 and a₁ = 6

Then:

aₙ = 6*(-2)^(n -1)

then:

a₅ = 6*(-2)^(5 - 1) = 6*(-2)^4 = 96

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!