write an explicit formula for arithmetic sequence

WRITE AN EXPLICIT FORMULA FOR ARITHMETIC SEQUENCE PLUS

Now the number of partyįavors she had before the second guest, well, The number of party favors Seo-Yun had before the first guest. G of n is going to be, or g of one is going to be So, when n is equal to one, when n is equal to one, So this is n, and then this is going to be g of n, right over here. All right, actually, before IĮven look at these questions, let me make a table hereīecause they're saying before the nth guest. Let n be a positive integer,Īnd let g of n denote the number of partyįavors Seo-Yun had before the nth guest arrived. To give away, and she gave away three partyįavors to each of her guests as they arrived at the party. Year and you multiply by 1.4 for any other year, any year other than n equals one. Going to multiply by 1.4 so B is going to be 1.4. Previous year grown by 40%, to grow by 40%, you're Previous year times what? It's going to be the Let's see, it's going to be the previous year, the Tree so A, this A over here, is 500, so A is 500, and then if we're not in the base case for any other year, we are going to have, Well, we know that when n equals one, we had 500 leaves on the Here, f of n is going to be equal to A when n is equal to one. And then they ask us, what are the values of the parameters AĪnd B for the sequence? So we have our base case So it's going to be in the geometric form. Well this is the arithmetic form, which we know isn't the case, Of the sequence can have one of the following two forms. To the question above, the recursive definition In this case, we're multiplying by 1.4, by 1.4 each time. Instead, we're multiplying or dividing by the same amount each time. Here, from 500 to 700, we grew by 200, and then from 700 to 980, we grew by 280. An arithmetic sequence, we would be adding or subtracting the same amount every time, but we're not. Notice it's definitely notĪn arithmetic sequence. Going to grow by 40% of 700, which is 280, so So 500 times 1.4, let'sĭo 40% of 500 is 200, so we're going to grow by 200, so we're going to go to 700. Now, when n is equal to two we're going to grow by 40%, which is the same thing as multiplying by 1.4. So when n is equal to one, the first year, n equals Let's make that a littleīit more tangible, just in case. Each successive term we're multiplying or dividing by the same number. Each successive year we're growing by 40%, that's the same thingĪs multiplying by 1.4.

What kind of sequence is f of n? So, some of you might be able to think about this in your head. The expression f of n defines a sequence.

The tree in Mohamed's back yard in the nth year Let n be a positive integer,Īnd let f of n denote the number of leaves on Each year thereafter, the number of leaves was 40% more than the year before. Just as we multiplied the first year by 1.4, we need to do it to the second year, the third year, … as the number of leaves grows each year.ĭecides to track the number of leaves on the tree in

Simply put each year’s number of leaves grows an additional 40% from the previous year’s total of leaves.

Why do we multiply the next year’s number of leaves by 1.4? Now I can clearly use the distributive property to factor 500 out of both terms giving me: To help illustrate that I will make an equivalent statement: I have two terms that both have 500 so I can factor the 500 out of both.

WRITE AN EXPLICIT FORMULA FOR ARITHMETIC SEQUENCE PLUS

the start of the second year) we will have 500 (our initial count) plus 200 (what grew during the year). We can determine that the count of 500 leaves would increase by 200 more leaves (40% of 500 = 200 0.4 * 500 = 200) during the first year. 2:30 Sal says “to grow by 40% you’re going to multiply by 1.4.' Okay, so why by 1.4? I’ll break it down and use 500 for my example.īeginning the first year there were 500 leaves.

Write an explicit formula for arithmetic sequence