Question

Each day he will fill 5 cups more. Write an algebraic expression to represent the number of cups he will have after n days. Identify the coefficient.

Answer 1

The question is not complete. Here is the complete question:-

Michael started by filling up 12 cups. Each day he will fill 5 cups more. Write an algebraic expression to represent the number of cups he will have after n days. Identify the coefficient.

Answer:

The algebraic expression is :

y = 12 + 5n

The coefficient is 5

Explanation:

Please kindly check the attached files for explanation

Answer 2

5n

The coefficient is 5

Explanation:

For day 1; he fill 5 cups

For day 2; he fill 5 + 5 cups

For day 3; he fill 5 + 5 + 5 cups

For day 4; he fill 5 + 5 + 5 + 5 cups

For day n; ?

The sequence is 5, 10, 15, 20, ...

The sequence increases linearly.

a = 5, d = 5, n = ?

Using the Formula for nth term of a sequence, we have:

`T_(n) = a + (n - 1)d\\T_(n) = 5 + (n - 1) 5\\T_(n) = 5 + 5n -5\\T_(n) = 5 - 5 + 5n\\T_(n) = 5n`