Find the sum of 20 (summation notation symbol)k=1 then (3k-5)
If you mean the sum of the first 20 terms, beginning with k=1, of
ak = 3k - 5,
that would be -20 x 5 = -100
PLUS the sum of the first 20 terms of
ak = 3k
The latter is 3 times the sum of
1+2+3+...20 ,
or 3*(20)(21)/2= 630
So the answer is 630 - 100 = 530
To find the sum of 20 terms using the summation notation, you can use the following steps:
1. Identify the formula for each term. In this case, the formula is given as ak = 3k - 5.
2. Write down the terms for k = 1 to k = 20:
a1 = 3(1) - 5
a2 = 3(2) - 5
...
a20 = 3(20) - 5
3. Calculate each term:
a1 = 3 - 5 = -2
a2 = 6 - 5 = 1
...
a20 = 60 - 5 = 55
4. Add up all the terms:
-2 + 1 + ... + 55 = 530
Therefore, the sum of the 20 terms is 530.
To find the sum of the series, 20 ∑(k=1) (3k - 5), we can break it down into two parts.
First, let's find the sum of the series (3k - 5):
∑(k=1) (3k - 5) = ∑(k=1) (3k) - ∑(k=1) (5)
To find the sum of the first part, ∑(k=1) (3k), we can use the formula for the sum of an arithmetic series:
∑(k=1) (3k) = n/2 * (first term + last term)
The first term (a) is 3(1) = 3, and the last term (l) is 3(20) = 60. So:
∑(k=1) (3k) = 20/2 * (3 + 60) = 10 * 63 = 630
To find the sum of the second part, ∑(k=1) (5), we can use the same formula:
∑(k=1) (5) = n * (first term)
The first term (a) is 5, and the number of terms (n) is 20. So:
∑(k=1) (5) = 20 * 5 = 100
Now, we can find the sum of the original series by subtracting the sum of the second part from the sum of the first part:
∑(k=1) (3k - 5) = 630 - 100 = 530
Therefore, the sum of 20 ∑(k=1) (3k - 5) is 530.