-5 | 6n +15 | +2 = - 43

n=-1 or n=-4

Step-by-step explanation:

-5/6n + 15/ = -45

/6n + 15/ = 9

square both sides to neutralize absolute value

/6n + 15/^2 = 81

36n^2 + 180n + 225 = 81

divide both sides by 9

4n^2 + 20n + 25 = 9

4n^2 + 20n + 16 = 0

divide both sides by 4

n^2 + 5n + 4 = 0

Factorize

(n + 1)(n + 4) = 0

therefore n = -1 or -4

4

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