Increasing and Decreasing Patterns

Q.

$\frac{1}{8}$, $\frac{1}{64}$, $\frac{1}{512}$, ........... is the increasing pattern.

1. False

2. True

Q. Why do we do for example 2 raised to the power of -2 so why do we write $\frac{1}{4}$?

Q.

$\frac{1}{5}$, $\frac{1}{25}$, $\frac{1}{125}$, ........... is the decreasing pattern.

1. True

2. False

Q.

which of the following is/are example/s for Decreasing pattern?

1. 2, $2^2$, $2^3$, $2^4$, ........

2. 3, $3^2$, $3^3$, $3^4$, ........

3. 4, $4^2$, $4^3$, $4^4$, ........

4. $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, .............

Q.

Which of the following is/are example/s for increasing pattern?

1. 2, $2^2$, $2^3$, $2^4$, ........

2. 3, $3^2$, $3^3$, $3^4$, ........

3. 4, $4^2$, $4^3$, $4^4$, ........

4. $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, .............

Q. Sort the following in the ascending order of their values from top to bottom.

1. $3^2$
2. $(-3{)}^3$
3. $2^3$
4. $2^2$

Q. The fibonacci sequence is defined by $a_1=1=a_2$ ;
$a_n=a_{n-1}+a_{n-2}$ for $n>2.$
Find $\frac{a_{n+1}}{a_n}$, for $n=1,2,3,4,5.$

1. $3,4,\frac{9}{2}$, $5$ and $8$
2. $1,2,\frac{3}{2},4$ and $8$
3. $1,2,\frac{3}{2}$ $,\frac{5}{3}$ and $\frac{8}{5}$
4. $1,2,\frac{3}{2}$ $6$ and $9$

Q. Arrange the following in ascending order of their values from top to bottom.

1. $2^0+3^0+4^0$
2. $4^1$
3. $3^1-2^0$
4. $(2+3+4{)}^0$

Q. $\frac{1}{2^5}\text{is greater than}\frac{1}{5^2}$.

1. False
2. True