# Find the total number of packets the pharmacy sold over the 16 weeks of the winter period?

## A pharmacy notices that their sales of cold medications increases steadily from the beginning of May. Their sales records show that last year they sold 26 packets of cold tablets in the first week in May. The sale of cold tablets increased by seven packets each week.

Jul 25, 2018

The pharmacy sold $1256$ packets

#### Explanation:

In the first week, the pharmacy sold 26 packets and the number of packets increased by 7 each week

so your pattern should look something like this:
$26 , 33 , 40 , 47 , 54 , \ldots$

Using arithmetic sequence, we can solve this question
${S}_{n} = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]$
where $a$ is your first number, $n$ is your nth term and $d$ is your difference between 2 adjacent terms

In this case,
$a$ is $26$
$d$ is $7$
$n$ is $16$ (since there are 16 weeks, then there should technically be 16 terms)

${S}_{16} = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]$
${S}_{16} = \frac{16}{2} \left[2 \times 26 + \left(16 - 1\right) \times 7\right]$
${S}_{16} = 8 \left[52 + 105\right]$
${S}_{16} = 1256$

ie $26 + 33 + 40 + 47 + 54 + 61 + 68 + 75 + 82 + 89 + 96 + 103 + 110 + 117 + 124 + 131 = 1256$