Sequences & Series Questions and Answers

Find the sum A wildlife refuge currently has 100 deer in it A local wildlife society decides to add an additional 2 deer each month It is already known that the deer population is growing 12 per year The size of the population is given by the recursively defined sequence Po 100 Pn 1 01pn 1 2 How many deer are approximately in the wildlife refuge at the end of the second month That is what is p 2 O1060 deer 109 deer 106 deer O111 deer

3 A grocery store worker has to collect all the shopping carts left out in the parking lot He collects 4 carts and measures the length of the 4 carts he is pushing to be 51 inches He collects another cart for a total of 5 carts and measures the length of the 5 carts to be 57 inches a He sees that there are a total of 21 carts in the parking lot How long will the line of 21 carts be

4a 2 marks Series Sequence Mia baked a very large apple pie that she cuts into slices to share with her friends The smallest slice is cut first The volume of each successive slice of pie forms a geometric sequence The second smallest slice has a volume of 30cm The fifth smallest slice has a volume of 240cm Find the common ratio of the sequence 4b 2 marks Find the volume of the smallest slice of pie 4c 2 marks The apple pie has a volume of 61425cm Find the total number of slices Mia can cut from this pie

2 Determine how many primes there are in the ranges 1 1000 1001 2000 and so on up to 9001 10000 Can you see why the Greeks might have wondered if they would run out Hint there are a number of websites that have lists of prime numbers Even easier use the Mathematica command Prime Pi k which gives the number of primes less than or equal to k

A retailer needs to purchase 10 printers The first printer costs 57 and each additional printer costs 3 less than the price of the previous printer up to 15 printers What is the total cost of 10 printers 552 90

Does this show an arithmetic or geometric sequence Write the recursive for the pattern shown PODL Arithmetic or Geometric ecursive Formula f 1 f n

the Democratic candidate Let X be the number of people who prefer the candidate when 31 people are surveyed at random pre a What is the distribution of X X Please show the following answers to 4 decimal places b What is the probability that exactly 16 voters who prefer the Democratic candidate in the survey c What is the probability that at most 16 voters who prefer the Democratic candidate in the survey d What is the probability that less than 16 voters who prefer the Democratic candidate in the survey e What is the probability that between 13 and 18 including 13 and 18 voters who prefer the Democratic candidate in the survey

Drag the tiles to the correct boxes to complete the pairs Not all tiles will be used Match each series with the equivalent series written in sigma notation n 0 n 0 2 9 n 0 n 0 3 2 3 5 7 0 n 0 3 4 2 3 3 15 75 375 1 875 2 6 18 54 162 n 0 4 32 256 2 048 16 384 3 12 48 192 768 4 4 n 0 5 3

ball is dropped from a height of 60 feet Each time it hits the ground It bounces two thirds of its evious height Find the total distance the ball has traveled before coming to rest 60 ft 40 ft 40 ft 26 7 ft 26 7 ft 17 8 ft 17 8 ft

Given a2 6 and a5 384 of a geometric sequence what is the recursive equation for the nth term an 4 an 1 a 1 5 an 4 an 1 a 1 5 an 4 an 1 a 1 5 an 4 an 1 a 1 5

Write the first six terms of the arithmetic sequence with the first term, a₁, and common difference, d. a₁ = 4, d = 1 a2 a3 24 = a5 = 0 86 = 0 a6 ...

Determine whether the sequence is arithmetic or geometric. Then find the next two terms. 1/2, 1, 3/2, 2.. Determine whether the sequence is arithmetic or geometric. Choose the correct answer below. Geometric Arithmetic 2,.. Write next two terms. 1/2, 1, 3/2, 2..

For each arithmetic series described below, write the series and calculate its sum. If it is not possible, explain why not. a. You know that the first term is 18, the last term is 72, and the common difference is 4.5. What is the series? What is the sum? b. You know that the series has nine terms and the last term is 18. What is the series? What is the sum? c. You know that the third term of an 18-term series is 29 and the terms are increasing by 10. What is the series? What is the sum?

Rosurvastatin/Crestor is a medicine used to decrease bad cholesterol and increase good cholesterol in the body. The half-life of Rosurvastatin is 1 day, which means that at the end of 1 day, half as much of the medication is left in your system. 1. If you take 60 mg of Rosurvastatin, how long do you think will it stay in your system?

Find a formula for the nº partial sum of the series series converges. The formula for the n A. The series converges. The series' sum is B. The series diverges. If the series converges, what is the series' sum? Select the correct choice below and fill in any answer boxes within your choice.

11. (a) Write the first 5 terms of a power series approximation for f(x) = e-x*² centered at X = 0. (b) Use the above power series approximation to find an approximation to S₁¹₁e-x² dx, rounding to 3 decimal places. Show work needed to produce this approximation. (c) Include a graph, shade the region corresponding to the integration and confirm your answer above using the computer or calculator to evaluate the integral.