Question 1081532
This is an arithmetic sequence. Take note how we add 6 each time to generate the next term (eg: 7+6 = 13, 13+6 = 19, etc)


The common difference is therefore d = 6.


The first term is 7, so {{{a[1] = 7}}}


The nth term {{{a[n]}}} is 


{{{a[n] = a[1]+d(n-1)}}}


{{{a[n] = 7+6(n-1)}}}


{{{a[n] = 7+6n-6}}}


{{{a[n] = 6n+1}}}


So the sigma notation summation would be


{{{sum(6k+1,k=1,10)}}}


Notice how plugging k = 1 leads to
6*k+1 = 6*1+1 = 7
which is the first term of the summation string "7+13+19+...+61"


while plugging k = 10 leads to
6*k+1 = 6*10+1 = 60+1 = 61
which is the last term of the summation string "7+13+19+...+61"


Note: solving 6k+1 = 61 leads to k = 10


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Final Answer: {{{sum(6k+1,k=1,10)}}}