Question

Alice is saving her chore money in a bank account. She makes a deposit of $13 in the first month.

Then every month, she deposits $25. Alice forms a sequence of her account balance, An where n
refers to the number of months. Which of the statements are correct about this sequence?
Select all that apply.

Answer 1

Option (3) and Option (5)

Explanation:

Alice invested $13 in the first month.

Then she deposits $25 every month.

Therefore, sequence formed by the deposit will be an arithmetic sequence.

First term of the sequence will be,

`A_1=13`

Since, recursive formula formula of a sequence is given by the formula,

`A_n=A_((n-1))+d`

Where 'd' = common difference in each term of the sequence

Recursive formula for the sequence will be,

`A_n=A{(n-1)}+25`

Since, explicit formula for the arithmetic sequence is represented by the formula,

`A_n=A_1+(n-1)d`

where n = number of term

d = common difference

Therefore, nth term of the sequence formed will be represented by the explicit formula,

`A_n=13+(n-1)25`

`A_(10)=13+(10-1)25`

= 13 + 225

= 238

`A_(8)=13+(8-1)25`

= 188

`A_(12)=13+(12-1)25`

= 288

Therefore, Option (3) and Option (5) will be the answer.