High School

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Amit starts a new bakery shop. To display the cakes, he puts:

- 3 cakes in the 1st row,
- 5 cakes in the 2nd row,
- 7 cakes in the 3rd row,

and so on.

Answer :

Amit displays the cakes in his bakery shop by arranging them in rows where each subsequent row has 2 more cakes than the previous row.

Amit's arrangement follows an arithmetic progression where the number of cakes in each row increases by 2.

This can be represented by the formula for the nth term of an arithmetic progression: [tex]\(a_n = a_1 + (n - 1) \cdot d\)[/tex], where [tex]\(a_n\)[/tex] is the nth term, [tex]\(a_1\)[/tex] is the first term, [tex]\(n\)[/tex] is the term number, and [tex]\(d\)[/tex] is the common difference.

In Amit's case, [tex]\(a_1 = 3\)[/tex] (the number of cakes in the first row) and [tex]\(d = 2\)[/tex] (since each subsequent row has 2 more cakes than the previous one). To find the number of cakes in any specific row, we can plug in the row number (n) into the formula. For example, for the 5th row, [tex]\(n = 5\)[/tex]:

[tex]\(a_5 = 3 + (5 - 1) \cdot 2 = 3 + 4 \cdot 2 = 3 + 8 = 11\).[/tex]

So, there would be 11 cakes in the 5th row of Amit's bakery shop display.

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Rewritten by : Barada