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When three quantities are in A.P., then the middle one is said to be the arithmetic mean of the other two. That is, if a, b and c are in A.P., then b is the arithmetic mean of a and c. Since a, b and c are in A.P., the common difference ought to be constant, we have
b - a
or b + b
or 2b
or b
We should remember that between any two quantities we can insert any number of terms so that the resultant series is in A.P. Now we look at some examples wherein we will insert the required number of terms.
Example
Insert 15 arithmetic means between 4 and 68.
We are given the first term and the last term. The total number of terms including 4 and 68 are therefore 17. Since "a" is given we ought to find "d". The 17th term is given by T17 = a + 16d = 4 + 16d. Also the T17 term is given to be 68. Therefore,
d
Using the values of "a" and "d" we insert the required terms. The series will be 4, 8, 12, ..., 68.
Using the example provided, Evaluate the area of the shaded region in terms of π. a. 264 - 18π b. 264 - 36π c. 264 - 12π d. 18π- 264 b. The area of the shaded r
Q. How to Convert Decimals to Percentages? Ans. Remember that when you have a decimal number, the digits to the right of the decimal point have the following meaning:
1. Which of the following is greater than 4.3 x 10^9 a. 2.1 x 10^9 b. 3.2 x 10^9 c. 5.3 x 10^9 d. 7.4 x 10^8 2. Which of the following is less than 6.5 x 10^-5 a. 1.4 x 10
Greatest Common Factor The primary method for factoring polynomials will be factoring the greatest common factor. While factoring in general it will also be the first thing
Luis runs at a rate of 11.7 feet per second. How far does he run in 5 seconds? You must multiply 11.7 by 5; 11.7 × 5 = 58.5. To multiply decimals, multiply generally, then coun
2/3=y-1/2
Consider the function f(x) = x + 1/x 2 + 2x - 3. (a) Find f(2) and f(-2). (b) Find the domain of f(x). (c) Does the range include 1? Show your working. (d) Find and si
I dont understand arcsin and arccos and how to find the domain...help?
how to solve the problems? methods to solve the question of joint lines
Maximize P=3x+2y Subject to x+y =6 x =3 x =0,y =0
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