explicit formula problem

Question

Malcolm's parents put $1,200 into a savings account when he was born in 2006. every birthday, Malcolm's parents deposit 10% more than the previous year.
Determine the explicit formula for the situation, assuming a(sub)0=2006

How much money is deposited into Malcolm's account in 2010, 2014, 2018, and 2022?

How much money do Malcolms parents contribute the year he turns 18?

What is the total amount of money Malcolm's parents have saved up at the end of 18 years?

Answer 1

beginning in 2006 and contributing additional money annually, the series of payments is

1200 +1.1(1200) + 1.1²(1200) + ... 1.1¹⁷(1200) for 18 years.

 

You should recognize this as a geometric series, so you can use the formula that applies.  The other questions can also be answered easily by calculating the appropriate individual terms.