We are given a finite series in summation notation and want to find its sum.
∑^6_(k=3) (5k-2)
Since the formula is a linear function of k, we know that the series is arithmetic. To calculate the sum we need to find the first and last terms. Let's substitute 1 and 6 for k in 5k-2.
a_k=5k-2
a_1=5( 1)-2
a_6=5( 6)-2
a_1=3
a_6=28
Now that we know a_1=3 and a_6=28, we will calculate the sum of the series by substituting a_1=3, a_n=28, and n=6 in the formula for the sum of a finite arithmetic series.
The sum of the first six terms of the series is 93. However, if we pay close attention to the given summation notation we can see that our series starts at n= 3. This means that we only want to calculate the sum from k=3 to k=6.
∑^6_(k= 3) (5k-2)
Since we already found the sum of all the terms, we will now calculate the sum of the first two terms and find the difference. We will start by finding the first term.
