Question 551086
All of your problems are sums of arithmetic sequences.
My problem is that I do not know what strategy you were expected to use to solve them. My way of solving them may not be what your teacher expects. You may be expected to look up a formula in your textbook and apply it, and the calculation may be different from the one I would do (same result, of course).
Your textbook or class notes may tell you that an arithmetic sequence can be represented as 
{{{a[1]}}}, {{{a[2]}}}, {{{a[3]}}}, .... {{{a[i]}}}, ...
with {{{a[i]=a[0]+id}}}
with the values of {{{a[0]}}} and {{{d}}} determining the sequence.
Then they could have said that
{{{sum( a[i], i=1, n )=sum( (a[0]+id), i=1, n )=n*a[0]+n*(n+1)*d/2}}}.
The way your problems read, you are given {{{a[0]}}}, {{{n}}}, and {{{d}}}, so that formula will work well.
Another formula you could have been given is
{{{sum( a[i], i=1, n )=n*(a[1]+a[n])/2}}}
That one is the easiest to derive for me (I don't memorize formulas; I just derive them from the definitions as needed). It would be easiest to use if you had the first and last terms already calculated.
You may have been given some other equivalent expression.
My best guess is that you are expected to use the first formula above, so I'll go with that.
51. {{{sum( (3+5i), i=1, 20 )=20*3+20*21*5/2=60+1050=1110}}}
(You could also say {{{a[1]=3+5=8}}}, and {{{a[20]=3+5*20=3+100=103}}}, so
{{{sum( a[i], i=1, 20 )=20*(8+103)/2=20*111/2=1110}}}, using the second formula).
52. {{{sum( (1+8i), i=1, 34 )=34*1+34*35*8/2=34+4760=4794}}}
53. {{{sum( (-10-3i), i=1, 15 )=15*(-10)+15*16*(-3)/2=-150-360=-510}}}
54. {{{sum( (6-(3/4)i), i=1, 22 )=22*6+22*23*(-3/4)/2=132-759/4=-57&3/4=-57.75}}}
55. {{{sum( (11+4i), i=1, 45 )=45*11+45*46*4/2=495+4140=4635}}}
56. {{{sum( (8.1+4.4i), i=1, 18 )=18*8.1+18*19*4.4/2=145.8+752.4=898.2}}}
Because I do not memorize formulas, I would have calculated it like this:
{{{sum( (3+5i), i=1, 20 )=3sum( 1, i=1, 20 )+5*sum( 3, i=1, 20 )=3*20+5*(1+20)*20/2=60+5*210=60+1050=1110}}}, splitting the sum into other sums, to make it easier to use the formula that makes more sense to me, but I bet that's not what your teacher expects.