Consider the rabbit pairs that illustrate the pattern in the Fibonacci sequence. These rabbits produce exactly 1 pair of new rabbits after reaching maturity at age 2 months. Imagine that the rabbits and all their offspring live forever. Also, imagine the field the rabbits live in can expand in size so that its side length is exactly equal to the number of pairs of rabbits living in the field. What is the side length of the field at the end of two years? Explain and show your work.

Q: The sum of n terms of two arithmetic progressions are in the ratio 5n +4 : 9n + 6. Find the ratio of…

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Q: Explain how notation in sequence works.

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Q: Find the day of the week you were born, and of your birthday this year.

A: We assume that on the date 01.01.01 the day was monday.  Now, from start of the years (01.01.01), We…

Q: Two positive numbers x and y are in the sequence 4, x, y, 12. The first three numbers form an…

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Q: 5 2² Find the sum of the first 8 terms in the sequence 5, 10, 20,....

A: I am attaching image so that you understand each and every step.

Q: Find the sum of a geometric progression whose first three terms are 12,-6, and 3. Show solution

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Q: 5) You get a new job with a beginning salary of $32,000 a year with a $1,000 raise every year. Let…

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Q: My birthday is on February 20, 2000 Find the day of the week you were born, and of your birthday…

A: According to the Zeller's Rule  F=k+ [(13*m-1)/5] +D+ [D/4] +[C/4]-2*C where k is the day of the…

Q: A car travels Ym, 7.5m, 11.25m and 16.875m in the first, second, third and fourth minute of its…

A: First of all we find the common ratio with the help of second,third,fourth term of the geometric…

Q: Consider the rabbit pairs that illustrate the pattern in the Fibonacci sequence. These rabbits…

A: Step:-1 Given that rabbits produce exactly 1 pair after 2 months. Let we have 1 pair of rabbits and…

Q: find the sum of the first 10 terms of geometric progression 2x,4x+14, 20x-14

A: Geometric progression: A sequence in which the next term is produced by multiplying a fixed number…

Q: Give a “real world” example of a situation where the infinite sum of a geometric pattern is equal to…

A: A real-world example of a situation where the infinite sum of the geometric pattern is equal to one.

Q: Find a 17 in the sequence 5, -10, 20, -40 ...

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Q: For which term does the geometic Sequence an = -36(?)^:/first have non-integer ralue a

A: Given, an=-3623n-1

Q: Given the sequence of numbers write a recursive equation 6, -2, -10, -18, -26,...

A: An arithmetic sequence is a collection of numbers in which repetition is allowed and an arithmetic…

Q: A ball is dropped from the height of 120 metres. After striking 4 a floor, the ball rebounds - th of…

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Q: Make poetry using fib sequence

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Q: 5. Calculate the formula for the geometric sequence 4000, 1000, 250, 62.5,

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Q: If term one = 93.19 and term 8 = 870.02 Show geometric progression for all 8 terms with working…

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Q: Find the general term in the sequence: 3, 13, 27, 45, 67.

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Q: Can the sequence 2, −4, 8, −16, 32, … be represented by an exponential function? Why or why not?

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Q: Sanjay's workday varies between 5 and 8 hours in length, based on the day's workload. If you make a…

A: calcxulation of above requirement with proper explanation are as follows

Q: Create your own sequence explicit formula.

A: Let, a sequence be: 2,4,8,16,32,64,... This sequence can be derived as  21=222=423=824=1625=32 and…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.