I have a test on this tomorrow and the way it's explained online is a bit confusing. If anyone can help, then please do so. I need to know what you would use this formula for, and how you would apply it to a problem. Also, what does each variable stand for?
-
The formula gives you any specific term, given the first term, a, specified n, as well as the ratio: r.
So a(1) should be a. Let';s check it. a(1) = a•r ¹⁻¹= ar° = a(1) = a
The third term, for example would be a(3) = a•r³⁻¹ = ar²
Suppose a = 2 and r = ½,
a(1) = a = 2(½)° = 2(1) = 2 --- as it should be.
a(2) = 2(½)¹ = 1
a(3) = 2(½)² = 2(¼) = ½
And so it continues.
The kth term would be a(k) = 2(½)ᵏ⁻¹
There is also a related RECURSION formula which gives you each term computed from the previuos term. a(n+1) = a(n)•r This recursion formula just says to fid the next term, justr take the cirrent term and multiply it by r. This is also referred to as the generating formula.
So a(1) should be a. Let';s check it. a(1) = a•r ¹⁻¹= ar° = a(1) = a
The third term, for example would be a(3) = a•r³⁻¹ = ar²
Suppose a = 2 and r = ½,
a(1) = a = 2(½)° = 2(1) = 2 --- as it should be.
a(2) = 2(½)¹ = 1
a(3) = 2(½)² = 2(¼) = ½
And so it continues.
The kth term would be a(k) = 2(½)ᵏ⁻¹
There is also a related RECURSION formula which gives you each term computed from the previuos term. a(n+1) = a(n)•r This recursion formula just says to fid the next term, justr take the cirrent term and multiply it by r. This is also referred to as the generating formula.