Question: In a geometric progression, the sum to infinity is five times the first term. a) Find the common ratio. b) The 2nd term is 12.

In a geometric progression, the sum to infinity is five times the first term.

a) Find the common ratio.

b) The 2nd term is 12. Find the 1st term.

c) Find the percentage difference between
the sum of the first ten terms and the sum
to infinity, correct to 3 significant figures.

Step by Step Solution

★★★★★

3.53 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

ANSWER a Let the first term be a and the common ratio be r Then the sum to infinity of a geometric p... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Complete Pure Mathematics Questions!

Q:

The fourth term of a geometric progression is 48 and the sum to infinity is five times the first term. Find the first term.

Q:

A geometric progression has first term a and common ratio r. The 1st, 2nd and 4th terms of the geometric progression form the first three terms of an arithmetic progression. a) Show that (r 1)(r + r...

Q:

1. [-/1 Points] DETAILS HARMATHAP12 6.2.010.MI. MY NOTES PRACTICE ANOTHER What interest will be earned if $6200 is invested for 6 years at 13% compounded monthly? (Round your answer to the nearest...

Q:

Please answer all of these questions in detail. Please explain as well. .ul TFW '6' 10:58 AM 2% C) i instructureuploads.33.amazonaws.com 2 Find the indicated sum. 25) Find the sum of the first 20...

Q:

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...

Q:

Question 16 5 pts Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. Find ag...

Q:

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...

Q:

1 Find the oth term of the geometric sequence with given first term a and common ratio r. a = -7, r= -5 an What is the fourth term? 24 =\fDetermine the common ratio , the fifth term, and the oth term...

Q:

Activity 1. Directions: Use the nth term of a geometric sequence ( = Q1"- to answer the following questions. 1. Find the seventh term in the geometric sequence 3, 6, 12, .. 2. Find the sixth term in...

Q:

Activity 1. Directions: Use the nth term of a geometric sequence ( = Q1"- to answer the following questions. 1. Find the seventh term in the geometric sequence 3, 6, 12, .. 2. Find the sixth term in...

Q:

The company Sabores y Sazones (S&S) has a limited stock of two herbs that are used in the production of dressings. S&S uses two ingredients HB1 and HB2 to produce either curry or paprika. The...

Q:

Create your own predictor, so you have to find or generate someRaw data: Data dimension should be at least 300x5 and larger Applymultiple linear regression steps, measure errors with differentmetrics...

Q:

By using _ _ _ _ _ an investor may experience an average share cost that is lower than the average share price in a fluctuating market . 1 . dollar cost averaging 2 . interest sweep 3 . automatic...

Q:

This continues exercise 1. (a) Here are the heights of four boys: 150 cm, 130 cm, 165 cm, 140 cm. Match the heights with the descriptions. A description may be used twice. unusually short about...

Q:

What test can be used to compare cancer incidence rates between the two treatment groups? Cancer The Physicians Health Study was a randomized doubleblind placebo-controlled trial of beta-carotene (50...

Q:

Implement the test in Problem 10.78, and report a two-tailed p-value. Cancer The Physicians Health Study was a randomized doubleblind placebo-controlled trial of beta-carotene (50 mg every other...

Q:

What is the best estimate of the probability of a male offspring based on the observed data? Demography A common assumption is that the gender distributions of successive offspring are independent....

Q:

In recent years, due to low interest rates, many homeowners refinanced their home mortgages. Linda Lahey is a mortgage officer at Down River Federal Savings and Loan. Below is the amount refinanced...

Q:

Mendosa Company closes its books monthly. On September 30, selected ledger account balances are: Notes receivable $33,000 Interest receivable $170 Notes Receivable include the following. Date Maker...

Q:

Suppose a riskless project requires an initial investment of $10 and will generate a one-time cash inflow of $30 two years later. Assuming a risk-free interest rate of 5%, which of the following...