Find the value of x in the figure below.

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.

(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

answer: -10

step-by-step explanation:

s(t) = 1 - 10t

s(x) = 1 - 10x

s(x + h) = 1 - 10(x + h)

            = 1 - 10x - 10h

s(x + h) - s(x) = 1 - 10x - 10h - (1 - 10x)

                      = 1 - 10x - 10h - 1 + 10x

                      = -10h

= -10