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}*{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}*{1.1^((7-1))}`

=
`{120}*{1.7715}`

= 212.58

Approximately

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