A geometric series has third term 27 and sixth term 8. a. Show that the common ratio

Question:

A geometric series has third term 27 and sixth term 8.

a. Show that the common ratio of the series is 2/3

b. Find the first term of the series.

c. Find the sum to infinity of the series.

d. Find the difference between the sum of the first 10 terms of the series and the sum to infinity. Give your answer to 3 significant figures.

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 07:59 AM

See More Questions

The first term of a geometric series is 30. The sum to infinity of the series is 240. a. Show that the common ratio, r, is 7/8. b. Find to 3 significant figures, the difference between the 4th and...
The third and fourth terms of a geometric series are 6.4 and 5.12 respectively. Find: a. The common ratio of the series. b. The first term of the series. c. The sum to infinity of the series. d....
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
Use a calculator to obtain solutions correct to the nearest hundredth in Problems 4954. x + 4 = 32x
Hemming Co. reported the following current-year purchases and sales for its only product. Required Hemming uses a perpetual inventory system. Determine the costs assigned to ending inventory and to...
Why does radioactive decay release heat, and which long-lived radioisotopes are responsible for planetary heating?
5. The simplified governmental fund accounting model is as follows: a Assets Liabilities Fund Balance b Current Assets Current Liabilities Fund Balance c Current Assets Noncurrent Assets ...
For each of the following records, indicate the appropriate related file structure: master file, transaction file, reference file, or archive file. a. Customer ledgers b. Purchase orders c. List of...
Grouper Corporation was organized on January 1, 2022. It is authorized to issue 15.000 shares of $100 per preferred stock and 549.000 shares of no-par common stock with a stated value of a pershare....
For each sequence: i. Write down the first 4 terms of the sequence ii. Write down a and d a un= 5n + 2 b u= 9 - 2n c un = 7+0.5n d un= n - 10
Find the first four terms of the following recurrence relationships. a Un+1=U+3, C U+1=2U e un +1 = = 1 = 3 2, = 10 bun+1=un-5, Uu = 9 d un+1=2u, +1, = 2 fun+1 = (u)-1, = 2
Using an example, explain how to factor out the greatest common factor of a polynomial.
On March 1 , Kerr Corporation issued 1 0 , 0 0 0 preferred shares for $ 1 0 0 per share. On July 1 5 , it issued an additional 3 0 , 0 0 0 shares for $ 1 2 0 per share. Each share is convertible into...
Hello, I need to calculate the break-even point in part B using the following formula: investment amount / (CLV of gold - CLV of platinum) . However, since that results in a negative value, does that...
Nervousness and depression are examples of __________ symptoms. psychophysiologic social health environmental psychological Roberta is using the structured format to present the results of his study...
Identify the stage of change the client is in and write in behavioral language at least one problem, with at least one goal and a minimum of two objectives for each goal for the client vignettes...
Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium-ion battery packs for a new line...
List some of the possible causes of a favourable direct material quantity variance?
Funds are separate fiscal and accounting entities, each with its own self-balancing set of accounts. The newly established Society for Ethical Teachings maintains two funds-a general fund for...
Answer Problem 5.6 for boys in this age range and economic environment? Suppose boys in this age range who live below the poverty level have a mean carbohydrate intake of 121 g/1000 cal with a...
Answer Problem 5.7 for boys in this age range and economic environment? Suppose boys in this age range who live below the poverty level have a mean carbohydrate intake of 121 g/1000 cal with a...
If we assume that the distribution of is normally distributed, then what % of (observer, trainer) pairs have a mean difference of 2 mm Hg in absolute value (i.e., either 2 mm Hg or 2 mm Hg)?...
1,600 Balance Sheet The following is a list (in random order) of KIP International Products Company's December 31, 2019, balance sheet accounts: Additional Paid-In Capital on Preferred Stock $2,000...
Question 3 4 pts 9 x + 3 x 9 if x 0 Find a) lim f(x), b) lim, f(x), C), lim , f(x) if they exist. 3 Edit View Insert Format Tools Table : 12pt M Paragraph B IV A2 Tv
Mr. Geoffrey Guo had a variety of transactions during the 2019 year. Determine the total taxable capital gains included in Mr. Guo's division B income. The transactions included: 1. On January 1,...

A geometric series has third term 27 and sixth term 8. a. Show that the common ratio

Question:

Step by Step Answer:

Lets denote the first term of the geometric series as a and the common ratio as r Given that the thi...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions