The sum of the first k terms in the sequence is 118096, find the value of k. the first term is 78732 the common ratio is 1/3.

k = 10

Step-by-step explanation:

The sum of k terms of a geometric sequence with first term a1 and common ratio r is given by ...

... Sk = a1·(1 -r^k)/(1 -r)

For the given numbers, this is ...

... 118096 = 78732·(1 -(1/3)^k)/(1 -1/3)

Manipulating this to get the term containing k, we have

... 1 -(2/3)(118096/78732) = (1/3)^k

... 1/59049 = (1/3)^k

Taking logarithms, we get

... -log(59049) = -k·log(3)

... log(59049)/log(3) = k = 10

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

is means division by fractions

step-by-step explanation: