Multiply the number by 4. add 10 to the product. divide this sum by 2. subtract 5 from the quotient.
the first number is 1 and the result is 2
the second number is 5 and the result is 10
the third number is 9 and the result is 18
the fourth number is 10 and the result is 20
write a conjecture that relates the result of the process to the original number selected. part a)
represent the original number as n.
answer is 2n
part b represent the original number as n, and use deductive reasoning to prove the conjecture in part (a). multiply the number by 4.
with part b .

step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

f(x) is   are being squared

g(x) is   increasing by 2

h(x) is adding .25 each time

k(x) is taking the square root

f(x) and k(x) are exponential functions