a. The fifth term of an arithmetic progression is 18 and the sum of the first eight

Question:

a. The fifth term of an arithmetic progression is 18 and the sum of the first eight terms is 186.

Find the first term and the common difference.
b. The first term of a geometric progression is 32 and the fourth term is 1/2.

Find the sum to infinity of the progression.

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

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

ISBN: 9781108407144

1st Edition

Authors: Sue Pemberton, Julian Gilbey

See More Books

Question Posted: Mar 10, 2023 06:35 AM

See More Questions

The fifth term of an arithmetic progression is 32 and the tenth term is 62. a. Find the first term and the common difference. b. The sum of all the terms in this progression is 350. How many terms...
The kth term of an arithmetic progression is given by u k = 12 + 4 k . a. Write down the first three terms of the progression. b. Calculate the sum of the first 12 terms of this progression.
The first term of an arithmetic progression is 12 and the sum of the first 16 terms is 282. a. Find the common difference of this progression. The first, fifth and nth term of this arithmetic...
A 1200-kg car has a maximum power output of 120hp. How steep a hill can it climb at a constant speed of 75km/h if the frictional forces add up to 650 N?
Why does high inflation typically destroy value for companies?
Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a sheer granite cliff of height 910 m in Yosemite National Park. Assume a jumper runs horizontally off the top of El...
Thirty-five consecutive samples of 100 bearings each, taken from a factory, had, respectively, 1, 2, 5, 3, 4, 2, 6, 8, 1, 2, 3, 9, 8, 0, 12, 10, 5, 4, 1, 8, 6, 7, 9, 4, 8, 1, 2, 6, 7, 5, 8, 1, 3, 4...
Financial statements for Pop Corporation and its 75 percent-owned subsidiary, Son Corporation, for 2017 are summarized as follows (in thousands): Pop Corporation acquired its interest in Son at book...
Resources Unlimited Corporation was formed in 1985 through the merger of two natural pipeline companies. The result was the largest gas distribution network in the United States, with 38,000 miles of...
Your division is considering two investment projects, each of which requires an up-front expenditure of $15 million. You estimate that the investments will produce the following net cash flows: (a)...
The first term of a geometric progression is 1 and the second term is 2 cos x, where Find the set of values of x for which this progression is convergent. 0
The first two terms, in ascending powers of x, in the expansion of Find the values of n , p and q. (1 + x) ( 2 4 ) are p+qx.
A hot-air balloon, headed due east at an average speed of 15 miles per hour and at a constant altitude of 100 feet, passes over an intersection (see the figure).Find an expression for the distance d...
Assume that a firm has weighted average cost of capital of 3.6% with a corporate tax rate of 21%. The pre-tax cost of debt is 3.1%. In case the firm would have no debt, the cost of equity for the...
Your grandmother will be giving you $10,000 every year for the next five years, the first payment beginning at the end of the first year A) If you invest these receivables in a bank at 6%, what is...
After the company issues an initial public offering and they desire to offer additional shares, one option is the seasoned equity offering. What are the differences between a convertible bond and a...
Can you explain how drilling and sampling are important in geotechnical engineering?
In a sewage system he diameter at Section 1 is 16 inches and the diameter at Section 2 is 8 inches. The flow rate through the pipe is 6 cfs. The pressure at Section 1 is 50 psi. What is the pressure...
Figure 8.18 shows that the short-run marginal cost curve may lie above the long-run marginal cost curve. Yet, in the long run, the quantities of all inputs are variable, whereas in the short run, the...
Rosalie owns 50% of the outstanding stock of Salmon Corporation. In a qualifying stock redemption, Salmon distributes $80,000 to Rosalie in exchange for one-half of her shares, which have a basis of...
Expand 10/(2 - x) 2 in ascending powers of x, up to and including the term in x 2 , simplifying the coefficients.
a. Factorise 2x 3 3x 2 3x + 2 completely. b. Hence express in partial fractions. x-13x-5 2x 3x-3x + 2
The first 3 terms in the expansion of (a 5x) 2 are 1/4 + 5/4x + bx 2 . Find the value of a, the value of b and the term in x 3 .
Nova Company s total overhead cost at various levels of activity are presented below: Month Machine - Hours Total Overhead Cost April 5 3 , 0 0 0 $ 2 1 4 , 4 3 0 May 4 3 , 0 0 0 $ 1 9 0 , 3 3 0 June...
Whirly Corporation s contribution format income statement for the most recent month is shown below: Total Per Unit Sales ( 7 , 4 0 0 units ) $ 2 3 6 , 8 0 0 $ 3 2 . 0 0 Variable expenses 1 3 3 , 2 0...
Olongapo Sports Corporation distributes two premium golf balls Flight Dynamic and Sure Shot. Monthly sales and the contribution margin ratios for the two products follow: Product Total Flight Dynamic...

a. The fifth term of an arithmetic progression is 18 and the sum of the first eight

Question:

Step by Step Answer:

a Let the first term of the arithmetic progression be a and the common difference be d Then the ...View the full answer

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

Students also viewed these Mathematics questions