We are given a finite arithmetic series in summation notation and want to find its sum.
∑^(10)_(k=0) (6k-1)
To calculate the sum, we need to find the first and last terms. Let's substitute 1 and 10 for k in 6k-1.
a_k=6k-1
a_1=6( 1)-1
a_(10)=6( 10)-1
a_1=5
a_(10)=59
Now that we know a_1=5 and a_(10)=59, we will calculate the sum of the series substituting a_1=5, a_k=59, and k=10 in the formula for the sum of a finite arithmetic series.
The sum of the terms a_1 to a_(10) of the series is 320. However, if we pay close attention to the given summation notation, we can see that our series starts at k= 0. This means that we want to calculate the sum from k=0 to k=10.
∑^(10)_(k= 0) (6k-1)
Since we already found the sum of ten of the terms in the series, we will now calculate the first term, a_0, and add its value to the sum.
