 Ex 1. If you were 65 and retired today, you would need about $1000 per month (again, in today’s money); but, with inflation, you will need more when you actually retire in about 50 years from now. Things will cost more in the future.
 Worstcase scenario, the inflation rate of 0.01 will need to be added to your future income. In other words, you will need an additional 1% of $1000 each month to make up for prices going up.
 If you plan to be in retirement for about 30 years, how much do you need to have in savings when you retire?
 Because this is only a partial sum (using inflation, a curved increase), we’ll need the partial sum formula.
 r: rate (0.01 + the whole amount); so, (1.01)
 is the 1st year:
 is the 2nd year:
 is the 3rd year:
 and so on…
 Setup:
 because 1000 divided by 0.01 equals 1000000.
 So, for 30 years, we will have 360 months: n = 360

 Answer: $3,495,000 is what you will need in savings to retire and live for about 30 more years.

 Ex 2. What is the value of the fourth term in a geometric sequence for which and ?
 Formula:

 Ex 3. The second term in a geometric sequence is 50. The fourth term in the same sequence is 112.5. What is the common ratio in this sequence?
 Formula:
 Setup: Since we don’t know the 1st term, let’s make 50 the 1st term for now. That makes 112.5 the 3rd term.
 Substitute:
 Simplify:
 Divide both sides by 50:
 Take the square root of both sides:

 Ex 4. What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/5? Answer using an improper fraction.
 Partial Sum Formula:
 Substitute:
 Simplify:
 Simplify More:
 Keep Change Flip:
 Cancel:
 Divide by to get the answer:

 Ex 5. The original value of a car is $18,000, and it depreciates (loses value) by 15% each year. What is the value of the car after three years?
 In this case, we are depreciating by 15% from the WHOLE value of the car. So, the rate is actually (10.15).
 Since we want the rate AFTER 3 years, we need to use n = 4 because we want to get 3 full years of depreciation and 4 – 1 = 3.

 Ex 6. A ball is dropped from a height of 12 feet and returns to a height that is onehalf of the height from which it fell.
 The ball continues to bounce half the height of the previous bounce each time.
 How far will the ball have traveled when it hits the ground for the fourth time?
 Setup: Do this by drawing. A ball drops 12 feet. When it hits the ground, that’s the 1st time.
 The ball goes up 1/2 way, so 6 feet, but then it comes back down. That’s the 2nd time it hits the ground (adding 12 feet from the 6 up and 6 back down).
 The ball goes up 1/2 way again, so 3 feet, then it comes back down. That’s the 3rd time it hits the ground (adding 6 feet from the 3 up and 3 back down).
 The ball goes up 1/2 way again, so 1.5 feet, then it comes back down. That’s the 4th time it hits the ground (adding 3 feet from the 1.5 up and 1.5 back down).
 Add up all the distance: 12 + 12 + 6 + 3.

 Ex 7. If your starting salary were $35,000 and you received a 6% increase at the end of every year for 16 years, what would be the total amount, in dollars, you would have earned over the first 16 years that you worked?
 Setup: Use the Partial Sum Formula to add up the TOTAL amount earned over 16 years.
 Answer: $898,538

 Ex 8. It is true that in a geometric sequence where r > 1, the terms always increase.

 Ex 9. It is true that in a geometric sequence, the term can be smaller than the term .
