Multiplication and division of each term of a ratio by the same non-zero number

Consider the following statements : 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP. Which of the above statements is/are correct?

Explain,by taking a suitable example,how the arithmetic mean alters by (i) adding a constant to each term,(ii) subtracting a constant from each them,(iii) multiplying each term by a constant and (iv) dividing each term by a non- zero constant

Multiplication of a non-zero rational number with an irrational number is an irrational number.

Division of fractions the division of a fraction (a)/(b) by a non - zero fraction (c)/(d) is defined as the product of (a)/(b) with the multiplicative inverse or reciprocal of (c)/(d)

Reciprocal of a non - zero rational number

To get the ratio p:q (for p!=q ) ,one has to add a number to each term of the ratio x:y ,the number is:

The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number lambda and then each of them is decreased by 25 their mean remains the same. Then lambda is equal to:

If the product of two non-zero rational numbers is 1, then they are (a)Additive inverse of each other (b)Multiplicative inverse of each other (c)Reciprocal of each other (d) Both (b) and (c)