Grade 11

Pre-Calculus 11 Week 1 – Arithmetic Sequences

alexr2015

First week of Pre-Calc 11! This week, I learned about Arithmetic Sequences.

Arithmetic sequences are like patterns, they look something like this: 5, 7, 9, 11, 13….

For a pattern to be an arithmetic sequence, all the numbers must have a common difference between them all. The common difference is how much it goes up or down. For our pattern here, the common difference is 2! You see how the pattern continues to increase by 2? This is an arithmetic sequence.

If you wanted to find the 20th term in that pattern, you would use the following formula:

t_10=t_1+9d

 

t_10 = 5 + 9(2)

 

t_10 = 5 + 18

 

t_10 = 23

With this formula, we’re saying that we’re going to take the first term in the arithmetic sequence, add the common difference (2) NINE times to get the 10th term. Let’s count it, and make sure my work is correct.

5, 7, 9, 11, 13, 15, 17, 19, 21, 23

Look at that, the 10th term really is 23! For this formula, you don’t have to use t1. You can use any term you already have. If we only had t4, the formula would look like this:

t_10=t4+6d

 

23 = 11 + 6(2)

 

23= 11 + 12

 

23 = 23

You can find a general formula for tn as well. It looks like this” $latex t_n = t1 + (n-1)d    For example:

t_23 = 5 + (23-1)d

 

t_23 = 5 + (22)2

 

t_23 = 5 + 44

 

t_23 = 49

 

Restaurant Reivew – Rosa’s Cucina Italiana

alexr2015

The household turned restaurant is small, but never felt cramped. Tables are spaced out nicely, while still making the most out of the space. There’s chatter amongst the tables, but it never overpowers your ears. Flags hang from the kitchen doors and around the restaurant, showing their nationality proudly. The walls are adorned, no, completely covered with pictures that Rosa has taken with many noteworthy people over the course of her life. They’re all signed by their respective celebrity, too. Michael Bublé, Wayne Gretzky, Bobby Hull, and many others. The only one that makes you a little uncomfortable is a picture of Ron Jeremy by the washroom doors with his, erhm, devilish smile. At least the picture was taken during his better years.

You and your friends sit down at a table, half of you sitting in booth seats, the others in chairs opposite of you. You feel comfortable in the leather seats that span the whole side of the restaurant wall. You order your food, and then are greeted by warm bread and butter while the main course is being prepared. Picking up the bread, you notice it is warm to the touch, but not burning your palm. Spreading butter on the bread, it melts perfectly on top. The bread warms your mouth. A crispy crust, but a fluffy inside. Perfect.

Finally, your dish arrives, catered to you by the waitress. The dish hasn’t even met your eyes, yet you can see the steam floating into the air from it. And it lands in front of you. Spaghetti covered with tomato sauce. Parmesan cheese splashed on top of the tomatoes, with some basil leaves on top to give it a splash of colour. A single, warm slice of garlic bread is set to the side of the dish. You smell the tomato sauce filling your nose with warmth. The scent of the garlic bread mixes with the rest of the dish nicely. The whole thing is such a pleasure to look at, you can hardly bring yourself to eat it! But you haven’t eaten anything since your 6-inch Subway sandwich for lunch, so you’re kinda hungry. You grab your fork and spoon, the required equipment for enjoying such a fine culinary creation. You wrap the spaghetti around your fork, raise it to your mouth, and bite.

The spaghetti itself; not too hard, but not practically made of mush. The perfect density. The tomato sauce and parmesan cheese compliment each other wonderfully. The tomato sauce brings your taste buds to a fiery awakening, while the parmesan cheese almost cools your mouth down and brings a second taste. The whole meal, instantly enjoyable, makes you feel like you’re in a restaurant in Italy. While your meal makes your wallet much lighter, your stomach and brain are only getting fuller. Full of enjoyable food and memories with your friends.