Find the sum of the summation if the upper limit is 50, k=1 and (3k+2)
To find the sum of the given summation, we need to calculate the sum of (3k+2) for every k starting from 1 up to 50.
The formula for the sum of an arithmetic sequence is given by:
Sn = n/2 * (a1 + an)
where:
- Sn is the sum of the arithmetic sequence,
- n is the number of terms,
- a1 is the first term, and
- an is the last term.
In this case, the first term is (3(1) + 2) = 5 and the last term is (3(50) + 2) = 152.
Now, we can substitute these values into the formula:
Sn = 50/2 * (5 + 152)
Sn = 25 * 157
Sn = 3925
Therefore, the sum of the summation when the upper limit is 50, k=1 and the term is (3k + 2) is 3925.