the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960

Question

06-07-2021
Mathematics

Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960

Sagot :

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.

Mexico experienced a series of liberal reforms in the 1860s instituted by Santa Anna. Benito Juarez. Porfirio Diaz. Lázaro Cárdenas.

Quadratic Equations: ax^2+bx+c=0 Factor first mult. A and C then use the factors from the answer to add to B 1.) 2b^2+10b+12 2.) 3g^2+8g+4 3.) 4x^2+4x-3 4.) 8b^

_______ is known as an activist president because he set the policies of his administration and sough to educate the public on national choices and priorities?

What has happened to Margaret Thatcher? What do people think about her? Does she have any connections with the Royal family?

A population of mice has black or brown hair. The gene for black hair color (B) is dominant over brown (b). If 16% of the mice are homozygous black and 24% are

How did John C. Calhoun of South Carolina view the power of the states and the power of the federal government? A.<===========My Guess He thought the federal

As a factory owner during the Industrial Revolution, write a letter to a newspaper justifying working conditions in your factory.

The Pacific Plate is located under the Pacific Ocean. Its movement has created the Island Arc and the Ring of Fire. This plate demonstrates ____________.

Sighting the top of a building, a surveyor measured the angle of elevation to be 60 degrees. The measurement is taken 200 feet from the building. Find the build

In Countries Where Businesses Are Government Owned?

Histrionicus Histrionicus · Answer 1 · 2021-07-12T02:40:12-04:00

Answer:

The correct answer is = 15.

Step-by-step explanation:

Formula:

The sum of the first n terms of an arithmetic progression with first term a and constant difference d is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]

using this formula in this problem

Solution:

The sum of the first ten terms is

[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]

[tex]S_{10}=5(2a+9d)[/tex]

The sum of the 20th, 21st, and 22nd terms is three times the 21st term:

[tex]3a_{21}=3(a+(21-1)d)[/tex]

[tex]3a_{21}=3(a+20d)[/tex]

[tex]3a_{21}=3a+60d[/tex]

The problem then tells us

[tex]S_{10}=3a_{21}[/tex]

[tex]10a+45d=3a+60d[/tex]

[tex]7a=15d[/tex]

there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is

then, 15, 22, 29, 36, ...

The problem says to find the number of terms n for which the sum is 960:

putting value in the formula

[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]

solving quadratic will give n = 15

thus, the correct answer is 15.

Sagot :

Other Questions