Question

A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 20% more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671

Answer 1

First term = a = 125

Explanation:

Question: find the number of shoppers on the first day

This is a geometric progression question

The sum of the terms = 671

Sum of a geometric sequence,Sn = (ar^n - 1) / (r - 1)

Where,

n = number of term in the sequence.

a = first term in the sequence.

r = common ratio

r = 1 + 20%

= 1 + 20/100

= 1 + 0.2

= 1.2

n = 4 (first 4 days)

Sn = (ar^n - 1) / (r - 1)

Sn = 671 where n = 4

671 = {a × 1.2^(4) - 1} / 1.2 - 1

671 = {a × 2.0736 - 1} / 0.2

671 = (2.0736a - a) / 0.2

671 = 1.0736a / 0.2

671 = 5.368a

Divide both sides by 5.368

a = 671 / 5.368

a = 125