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Beginning with Rodney’s first month of high school, his father deposits $5 into Rodney’s savings account. Each month after the first month, his father deposits $2 more than the previous month. The total amount deposited in Rodney’s account after four years can be represented using the expression . How much total money has been deposited?
$2,496
$2,544
$2,640
$2,688

Answer :

bastianclark

Answer:

A

Step-by-step explanation:

Edge 2021

The sum of the 48 terms will be $2,496. Then the correct option is A.

What is the arithmetic sum of sequence?

Let a₁ be the first term, n the number of the terms, and l be the last term of the sequence.

Then the sum of all the terms will be given as,

S = [n (a₁ + l )] / 2

Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as

[tex]\rm a_n = a_1 + (n - 1)d[/tex]

Beginning with Rodney’s first month of high school, his father deposits $5 into Rodney’s savings account.

Each month after the first month, his father deposits $2 more than the previous month.

Then the first term is $5 and the common difference is $2.

The total amount deposited in Rodney’s account after four years can be represented using the expression.

Then the total number of the terms will be

n = 4 x 12

n = 48 months

Then the 48th term of the sequence will be

a₄₈ = 5 + (48 – 1) · 2

a₄₈ = 5 + 47 · 2

a₄₈ = 5 + 94

a₄₈ = 99

Then the sum of the 48 terms will be

S = 48 (5 + 99) / 2

S = 24 × 104

S = $2,496

Then the correct option is A.

More about the arithmetic sum of sequence link is given below.

https://brainly.com/question/14021449

#SPJ5

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