Question

The function n(d)=4⋅3d−1 represents the number of people who receive a newspaper on day d of a delivery schedule.

Answer 1

The answer is 'The number of people receiving a paper on a given day is 3 times what it was the previous day.'

Answer 2

The relation between number of people who receive a newspaper on day d of a delivery schedule is given by:

n(d) = 4.3 d - 1

On first day , i.e d =1

n = 4 × 3 -1

   = 12 -1

   = 11

For, d =2

n(d) = 4 × 3 × 2 -1

      = 24 -1

      = 23

for , d=3

n(d) = 4 × 3 × 3 - 1

       = 36 -1

       = 35

When , d = 4

n(4)= 4 × 3 × 4 - 1

     = 48-1

     = 47

n(5) = 4×3×5 -1

       = 60 -1

        = 59

As you can see the pattern ,the number of people who receives newspaper starting from day = 1,2,3,4,5,6,7.... is 11,23,35,47,59,71,83,.......

As the given sequence is Airthmetic progression , having , a = 11

d = 23 -11= 12,

$a_{n}$ = 11 +12 × (n-1)

                        = 11 + 12 n - 12

                         = 12 n - 1

                          = 4 × 3 × d - 1    →→n is replaced by d