The larger of two consecutive ODD numbers is one less than twice the smaller number. Find the larger of the two numbers.

Step-by-step explanation:

z -  any integer

2z+1 - any odd integer (the smaller one)

2z+1+2 = 2z+3 - odd integer consecutive to 2z+1  (the larger one)

2(2z+1)    - twice the smaller number

2(2z+1) - 1    - one less than twice the smaller number

2(2z+1) - 1 = 2z + 3

4z + 2 - 1 = 2z + 3

2z = 2

 z = 1

2z+3 = 2•1+3 = 5

check:

2z+1 = 2•1+1 = 3,  

2(2z+1)-1 = 2(2•1+1)-1 = 2•3-1 = 5 = 2z+3

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.