Mohamed decided to track the number of leaves on the tree in his backyard each year. The first year, there were 500500500 leaves. Each year thereafter, the number of leaves was 40\%40%40, percent more than the year before. Let f(n)f(n)f, left parenthesis, n, right parenthesis be the number of leaves on the tree in Mohamed's back yard in the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript year since he started tracking it. fff is a sequence. What kind of sequence is it? Choose 1

Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500 leaves. each year thereafter, the number of leaves was 40% more than the year before. let f(n) be the number of leaves on the tree in Mohamed's backyard in the n^th year since he started tracking it. f is a sequence. what kind of sequence is it?

Number of leaves on the tree in first year = 500

The number of leaves was 40% more than the year before.

So rate of increase is 40/100 = 0.4

We use exponential growth formula,

f(n) = a(1+r)^n

Where a is the initial number, r is the rate of growth, n is the number of years

We know a= 500, r= 0.4

f(n) = 500(1+0.4)^n

f(n) = 500(1.4)^n

Plug in n=1,2,3...

f(1) = 500

f(2) = 500 * 1.4^1

f(3) = 500 * 1.4^2 and so on

From this we can see that the common ratio is 1.4

Hence it is a Geometric sequence.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for