Show work plz hahaha

you borrow money for a new car from the bank. after month 1, the loan balance is $14,760. after month 2, it is $14,520. if this pattern continues, what will the balance be after 21 months?

The balance after 21 months is  $9960.

Let a₁ = 14760, a₂ = 14520, and a₂₁ be the balance after 21 months:

So we apply the given values to get the missing values:

First, we get the common difference, That is,

d = a₂ - a₁

d = 14520 - 14760

d = -240

So, we substitute the value of common difference and the known values,

a₂₁ = a₁ + (n-1)d

a₂₁ = 14760 + (21-1)(-240) 

a₂₁ = 14760 + (20)(-240) 

a₂₁ = 14760+(-4800)

a₂₁ = 9960

Therefore, the balance after 21 months is  $9960.