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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.
Add 1011 and 1101 in base 2
Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2, Subject to the constraints: X1+ X2 = 4 X1+ X2 = 2 X1, X2 = 0
( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5 4bx- 2by = - 1
Function of a Function Suppose y is a function of z, y = f(z) and z is a function of x, z = g(x)
assinment
which ne is greater -4 4/25 or -4.12?
#There is a balance of $1,234 and this person receive a refund check in the amount of $25 with her paycheck that was deposited into her account for $1500 which made her balance $27
Ionic solids, which have anionic vacancies because of metal excess defect develop colour. Illustrate with the help of a suitable example.
Question: Find all third order partial derivatives for the function F(x,y)= log xy+ e (x+y) -x/y.
TYPES OF INFINITY : Mostly the students have run across infinity at several points in previous time to a calculus class. Though, when they have dealt along with this, this was jus
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