You have a large collection of 1 × 1 squares and 1 × 2 dominoes. You want to arrange these to make a 1 × 15 strip. How many ways can you do this? Start by collecting data. How many length 1 × 1 strips can you make? How many 1 × 2 strips? How many 1 × 3 strips? And so on. How are the 1 × 3 and 1 × 4 strips related to the 1 × 5 strips? How many 1 × 15 strips can you make? What if I asked you to find the number of 1 × 1000 strips? Would the method you used to calculate the number fo 1 × 15 strips be helpful?

Step-by-step explanation:

To solve this strip question, there’s a need to draw a strip diagram (which is a rectangular mathematical presentation that is used to show arithmetical relationships and may also be used for fractions representation or solve problems that involves operations.)

Kindly check the attached images below to see the step by step explanations to the above question

can i see the following ?

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