Question

A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the

number of shoppers is 10% more than the number of shoppers the day before.

What is the total number of shoppers that visited the mall in the first 7 days?

Round your final answer to the nearest integer.

Answer 1

$\boldsymbol{\mathbf{Answer}}$

$\boldsymbol{\mathbf{213\,shoppers\, will\, visit\,on \, first\, seventh\, day}}$

$\boldsymbol{\mathbf{Step-by-step explanation}}$

Let, No of shoppers on first day = a

No of shoppers on second day = b

Similarly till seventh day,

Therfore shoppers on seventh day=

a + b + c + d + e + f + g

As mentioned ,number of shoppers is 10% more than the number of shoppers the day before. i.e we can understand that a to g all are 1.1 times bigger than the previous letter.

That means all are in geometric series.

We know the formula for sum of geometric series is,

=$\boldsymbol{\mathbf{\sum {a}\times{r^{(n-1)}}}}$

$\boldsymbol{\mathbf{a \, is\, first\, value}}$

$\boldsymbol{\mathbf{r \, is\, multiplication\, factor\, value}}$

$\boldsymbol{\mathbf{n \, is\, no\, items\, in\, series}}$

That is,

a = 120

r = 1.1

n = 7

=$\sum {120}\times{1.1^{(7-1)}}$

=${120}\times{1.7715}$  

= 212.58

Approximately

$\boldsymbol{\mathbf{=\, 213 \,shoppers \,will\, be \,there\, on \,seventh \,day.}}$