20 pts! ? trig

if sec(a) = 3/2 and < a is in the quadrant i, what is the value of tan(x)?

a. 2sqrt5 /3

b. sqrt5 /3

c. sqrt5 /2

d. 3sqrt5 /2

give me a short or long explanation on how to solve this if you can .

answer is x<

(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