Sequence is a succession of numbers formed according to some fixed rule. Example is
which is a sequence so that the nth term is given by n3.
Series is the indicated sum of a sequence of numbers. Thus,
is the series corresponding to the sequence $a_1,~ a_2,~ a_3,~ ... ,~a_n,~ ...$
Finite and Infinite Series
Problem
The sum of the digits of a three-place number is 19. If the tens and units digits are interchanged the number is diminished by 27, and if the hundreds and tens digits are interchanged the number is increased by 180. What is the number?
Problem
The sum of the parents' ages is twice the sum of their children’s ages. Five years ago, the sum of the parents' ages was four times the sum of their children’s ages. In fifteen years, the sum of the parents' ages will be equal to the sum of their children’s ages. How many children were in the family?
Problem
Alfred is four times as old as his nephew Franco. 5 years ago, the sum of their ages is equal to the present age of Alfred. How old is each?
Problem
What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?
A. 2:18:27.6
B. 2:16:00.0
C. 2:17:56.3
D. 2:19:03.1
Coin denominations in the US
| Name | Coin value | Dollar Equivalent |
| Penny | 1 ¢ | \$0.01 |
| Nickel | 5 ¢ | \$0.05 |
| Dime | 10 ¢ | \$0.10 |
| Quarter | 25 ¢ | \$0.25 |
| Half-dollar | 50 ¢ | \$0.50 |
There are 12 dial units in the clock. Every time the minute hand completes 12 dials, the hour hand moves 1 dial. Thus, if the minute hand moves by x the hour hand moves by x/12.
Key equations:
$\dfrac{x}{12}$ = distance traveled by the hour hand (in minutes)
Case 1: Workers have different rates
Work rate = (1 job done) / (Time to finish the job)
Time of doing the job = (1 job done) / (Work rate)
For example
Albert can finish a job in A days
Bryan can finish the same job in B days
Carlo can undo the job in C days
If x = present age of a person
x – 3 = age of the person 3 years ago
x + 5 = age of the person 5 years from now or 5 years hence
Note:
The difference of the ages of two persons is constant at any time.
Motion with constant velocity
The distance traveled is the product of velocity and time.
were,
s = distance
v = velocity
t = time
It follows that
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