Question

Ronald Dairo is helping the local indus-

try in promoting papaya rosette. On the first
day, he produces 5,890 pieces of papaya
rosette, 7,020 pieces on the second day
8,150 pieces on the third day, and so on.
How many pieces of papaya rosette can Mr.
Dairo produce in 2 weeks?
As part of the annual Pagdihon Festival.

Answer 1

Mr. Dairo can produce 20580 pieces of Papaya rosette in two weeks.

Explanation:

Papaya rosette pieces on first day = 5890

Papaya rosette Pieces on second day = 7020

Papaya rosette Pieces of third day = 8150

Let

`a_1 = 5890\\a_2 = 7020\\a_3 = 8150`

We can check if these numbers are part of a sequence.

In order to check, common difference will be found first.

`d = a_2-a_1 = 7020-5890 = 1130\\d =a_3-a_2 = 8150-7020 = 1130`

It can be observed that the common difference is same. When the common difference is same, the sequence is said to be an arithmetic sequence.

The formula for arithmetic sequence is given by:

`a_n = a_1+(n-1)d`

Putting the values

`a_n = 5890+(n-1)(1130)\\a_n = 5890+1130n-1130\\a_n =4760+1130n`

The formula for nth term can be used to find any term. As we have to find the number of papaya rosette pieces after two weeks which means that we need to find the number of pieces on 14th day.

So,

`a_(14)= 4760+1130(14)\\a_(14) = 4760+15820\\a_(14) = 20580`

Hence,

Mr. Dairo can produce 20580 pieces of Papaya rosette in two weeks.