A geometric series has first term a and common ratio r The second term of the series is 11 8 and the sum to infinity of the series is 8 a Show that 64r 2 64r 15 0 b Find the two possible values of r c Find the corresponding two possible values of a Given that r takes the smaller of its two possible...

A geometric series has first term a and common ratio r. The second term of the series

Question:

A geometric series has first term a and common ratio r. The second term of the series is 11/8 and the sum to infinity of the series is 8.

a. Show that 64r² − 64r + 15 = 0.

b. Find the two possible values of r.

c. Find the corresponding two possible values of a. Given that r takes the smaller of its two possible values,

d. Find the smallest value of n for which S_n exceeds 7.99.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

See More Books

Question Posted: Aug 08, 2023 07:58 AM

See More Questions

a. The sixth term of an arithmetic progression is 35 and the sum of the first ten terms is 335. Find the eighth term. b. A geometric progression has first term 8 and common ratio r. A second...
A convergent geometric series has first term a and common ratio r. The second term of the series is 3 and the sum to infinity of the series is 6.75. a. Show that 27r 2 27r 12 = 0. b. Given that the...
a. The seventh term of an arithmetic progression is 19 and the sum of the first twelve terms is 224. Find the fourth term. b. A geometric progression has first term 3 and common ratio r. A second...
In his book Future Shock, Alvin Toffler divided humanitys time on earth into 800 lifetimes. The 800th lifetime, in which we now live, has produced more knowledge than the previous 799 combined, and...
The July transactions of Acorn Industries are described in Problem 7- 1B. In Problem 7- 1B, Acorn Industries completes these transactions during July of the current year (the terms of all its credit...
Garlington Technologies Inc.'s 2015 financial statements are shown below: Balance Sheet as of December 31, 2015 Income Statement for December 31, 2015 Sales...
Germicidal lamps are used to sterilize tools in biological and medical facilities. One type of germicidal lamp is a low-pressure mercury discharge tube, similar to a fluorescent lightbulb, that has...
Perot Corporation is developing a new CPU chip based on a new type of technology. Its new chip, the Patay2 chip, will take two years to develop. However, because other chip manufacturers will be able...
Please discuss stock valuations, provide examples of how a company uses them, and presents 3 methodologies to calculate the stock value. 1) Briefly compare and contrast the Dividend Discount Model...
I invest A in the bank at a rate of interest of 3.5% per annum. How long will it be before I double my money?
An arithmetic sequence has first term k 2 and common difference k, where k > 0. The fifth term of the sequence is 41. Find the value of k, giving your answer in the form p + q 5, where p and q are...
What is the value chain? Describe, in sequence, the main components of a manufacturers value chain.
One of the issues that is debated in virtually every election is whether to raise the federal minimum wage, which stood at $7.25 per hour in 2018. Suppose that you are married with a child, working a...
How would you expect the possibility of differentiating your product to change competition between oligopolists?
The 2018 federal poverty guidelines used to determine eligibility for Medicaid and the Childrens Health Insurance Program (CHIP) set a poverty line of $25,100 for a family of four in the 48...
As corruption falls in a country, cost of production often falls. Why?
Conduct an online search for iPhone repair San Diego You will find about 10 million entries. Now try iPhone screen repair San Diego. You will find more than 6 million entries. Try to estimate the...
Write balanced equations for each of the following processes. a. Chromium-51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture. b....
A test car is driven a fixed distance of n miles along a straight highway. (Here n Z+.) The car travels at one mile per hour for the first mile, two miles per hour for the second mile, four miles...
What is the probability that at least 3 of 5 light users are HIV positive? Infectious Disease A study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of...
Suppose we have a group of 10 light users and 10 heavy users. What is the probability that exactly 3 of the 20 users are HIV positive? Infectious Disease A study considered risk factors for HIV...
What is the probability that at least 4 of the 20 users are HIV positive? Infectious Disease A study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of...
Consider the following behavior of a sequential logic. A state machine for this behavior has one input named X, one output named Z, and a 2-bit register for the state information. Assume that the...
Consider the graphs on the right, which we denote as a cycle and an in- finite diamond strip (IDS). The cycle has n nodes V1, Unvo that are consecutively ordered, i.e., vi has vi-1 and vi+1 mod n as...
Use the generic graph I h(x) 3 A 6 B 5 B 4 1 5 C 2 3 D 2 E 1 F F 0 34 search method covered in class, carry out BFS, DFS, uniform-cost, and A* over the graph and the heuristic function given in the...

A geometric series has first term a and common ratio r. The second term of the series

Question:

Step by Step Answer:

a ar b 15 8 8 a ...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions