S3-S2 = term 3
S3 = 13/17
S2 = 8/12
maybe 13/17 - 8/12 ??? about .098
∞
Σan is Sn = (5n-2)/(5n+2)
n=1
Find a3. I have tried plugging in n = 3 and solving Sn but that is incorrect. I believe something is wrong with my approach and I would be happy to get some guidance.
S3 = 13/17
S2 = 8/12
maybe 13/17 - 8/12 ??? about .098
The formula for the nth partial sum is given by:
Sn = (5n - 2) / (5n + 2)
To find a3, we can plug in n = 3 into the formula:
S3 = (5(3) - 2) / (5(3) + 2)
Simplifying this expression gives us:
S3 = (15 - 2) / (15 + 2)
S3 = 13 / 17
Therefore, a3 = 13.
Let's start by examining the given series sum formula:
Sₙ = (5n - 2) / (5n + 2)
The subscript, n, represents the term numbers of the series. In our case, we want to find the third term, so n = 3.
Now let's substitute n = 3 into the series sum formula:
S₃ = (5(3) - 2) / (5(3) + 2)
= (15 - 2) / (15 + 2)
= 13 / 17
Therefore, the value of the third partial sum, S₃, is 13/17.
However, it seems there might be some confusion, as the term a₃ represents the value of the third term of the given series (not the partial sum). To find a₃, we can find the difference between consecutive partial sums.
a₃ = S₃ - S₂
To find S₂, we can substitute n = 2 into the series sum formula:
S₂ = (5(2) - 2) / (5(2) + 2)
= 8 / 12
= 2 / 3
Now, let's calculate the value of a₃:
a₃ = S₃ - S₂
= (13/17) - (2/3)
= (39 - 34) / (51)
= 5 / 51
Therefore, the value of a₃ is 5/51.
To recap:
- The value of the third partial sum, S₃, is 13/17.
- The value of the third term, a₃, is 5/51.