When facing problems where you have to find a certain term of a sequence, look really closely for patterns. Some sequences have a really easy pattern like adding or subtracting numbers. Other sequences have more complicated patterns.
In this case, based solely on the three numbers you are given you can observe that the numbers are decreasing.
Here's what we can see so far:
To get from the 1st term to the 2nd term:
subtract 5 from the starting number
To get from the 2nd term to the 3rd term:
subtract 6 from the above result
Even though we only have a small piece of the pattern, let's try extending it! We're going to continue subtracting, but we're going to increase the amount that we take away every time.
Try solving it yourself before you look ahead! :)
So continuing the pattern:
Start at -4
To get from the 1st term to the 2nd term:
subtract 5
(-4 - 5) = -9
To get from the 2nd term to the 3rd term:
subtract 6
(-9 - 6) = -15
To get from the 3rd term to the 4th term:
subtract 7
(-15 - 7) = -22
To get from the 4th term to the 5th term:
subtract 8
(-22 - 8) = -30
To get from the 5th term to the 6th term:
subtract 9
(-30 - 9) = -39
[...continue this pattern until you reach the 17th term...]
Before you just write down the answer, make sure you do your own work! I calculated that the 17th term was -204.
Try practicing with some other sequences of numbers! You've got this!
Answer: Molly will have to save $10 each week for 9 weeks to get $189.
Step-by-step explanation:
Start at $99, count $10 every week until you get $189. Your answer is 9 weeks.
Answer:
5/2
Step-by-step explanation:
the equatino you are using is point slope form which is an equation involving the points and the slope and the origonal equation is y-y1=m(x-x1) m standing for slope, and x1 and y1 standing for the first coordinates, so the slope would be 5/2
Answer: A recursive formula would be best to describe the pattern.
Step-by-step explanation: The pattern of numbers in the question clearly indicates it is an arithmetic progression, that is, every number is derived by adding a common difference to the previous number. The common difference or d, does not change throughout the sequence.
The common difference in the sequence above is 2. Upon close observation we would observe that by simply adding 2 to a number we can arrive at the next number.
However, using words to describe the pattern of the sequence would not be helpful if we have to find a number very far into the sequence, for example if we were to find the 1000th term of the sequence.
A recursive formula is preferable and would be the best option because of its simplicity in application. The recursive formula to calculate the nth term of an arithmetic progression is given as
nth = a + (n - 1)d
Where n is the term to be calculated in the sequence (in this case n equals 50), a is the first term (2 in this case) and d is the common difference (2 in this case).
The 50th term can be calculated as follows;
nth = 2 + (50 - 1)2
nth = 2 + (49)2
nth = 2 + 98
nth = 100
The calculation above shows how simple it is to calculate the nth term with a recursive formula rather than with verbal descriptions.
An explicit formula also allows you to find the value of any term in a sequence. The explicit formula designates the nth term of the sequence as an expression of n, that is, it defines the sequence as a formula in terms of n. This formula lets us find any other term without knowing other terms.
Answer:
It should be 
Step-by-step explanation:
