Question

Aliyah plays an online learning game where she earns 10 stars for each question she answers correctly. When Aliyah

finishes playing the game, she has a total of 570 stars.
Write an equation for this arithmetic sequence in the form an = a, + d(n-1) that can be used to model the number
of stars Aliyah ears when she answers n questions correctly.

Answer 1

CASE I:

`a_1 = 10`

`a_n =a_1+10(n-1)`

CASE II:

`a_1 = 570`

`a_n =a_1+10(n-1)`

Explanation:

CASE I: We start counting when Aliyah starts the game.

For the first question she answers Aliyah earns 10 points; therefore,

`a_1 = 10`.

And for every additional nth answer, Aliyah earns 10 additional points; therefore,

`a_n = a_1+10(n-1)`

`\boxed{a_n =10+10(n-1)}`.

CASE II: We start counting after Aliyah finishes the first game.

In which case

`a_1 = 570`

and therefore,

`\boxed{a_n = 570+10(n-1)}`