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The rule for the sequence is S(n) = 2S(n-1) - S(n-2)
Alternative form: S(n) = S(n-1) + 3
Step-by-step explanation:
In this problem, we know the first two terms of the sequence:
S(1) = 2
S(2) = 5
We are told that each term after the second is created by subtracting the term before the previous term from twice the previous term. In other words, if we call:
S(n) the current term
S(n-1) the previous term
S(n-2) the term before the previous term
This statement translates into the following sequence:
S(n) = 2S(n-1) - S(n-2)
Because we are subtracting the term before the previous term, S(n-2), from twice the previous term, 2S(n-1).
We can apply now the rule to find the first few terms of the sequence after S(1) and S(2):
We notice also that each term of the sequence is just equal to the previous term plus 3, so the sequence can also be written as
S(n) = S(n-1) + 3
Learn more about sequences:
#LearnwithBrainly
Answer:
<em>OR </em><em>in </em><em>Decimal</em>,
Step-by-step explanation:
<u>Given:</u>
Two points, that is (5,3) & (8,5)
<u>To Find:</u>
The Distance of the two given points
<u>Solution:</u>
To Find the distance between two points, we will use the <u>distance</u> <u>formula</u>, i.e. :
According to the Question,
Now Substitute the values on the formula of Distance and then Simplify:
<em>[Follow PEMDAS rule while simplifying]</em>
Hence, the distance between the two given points would be or
.
I hope this helps!
Have a good day! :)
<em>[Desmos Graph solution is attached]</em>
