For n ≥ 1, let S be a set containing 2n distinct real numbers. By an, we denote the number of comparisons that need to be made between pairs of elements in S in order to determine the maximum and minimum elements in S. Requried:
a. Find a1 and a2
b. Find a recurrence relation for an.
c. Solve the recurrence in (b) to find a formula for an.

A) = 1, = 4

B) = 2 + 2

C)    

Step-by-step explanation:

For n ≥ 1 ,

S is a set containing 2^n distinct real numbers

an = no of comparisons to be made between pairs of elements of s

A)

= no of comparisons in set (s)

that contains 2 elements = 1

= no of comparisons in set (s) containing 4 = 4

B)  an = 2a + 2

C) using the recurrence relation

a = 2a + 2

substitute the following values  2,3,4  .......... for n

a = 2a + 2

a = 2a + 2 =

a =

    =   ---------------- (x)

since  2^1 + 2^2 + 2^3 + ...... + 2^n-1 =  

applying the sum formula for G.P

Note ; a = 2, r =2 , n = n-1

a1 = 1

so equation x becomes

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9