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I like the doubt it made me think for a while so here's what i did
for 8) i found the sum of n=1,n=2 and n=3 i could keep going just to be more sure but 3 are enough
i found sum of 1st n terms is -1
sum of 2nd n terms is 4
sum of 3rd n terms is 15
as we know sum of 1st term is -1 that makes it obvious first term is -1
so we have -1,y,z
y and z are 2nd and the 3rd term respectively
as we know sum of 2nd n terms is 4 that means -1+y=4
and so for the 3rd -1+y+z=15
we will get y=5 and z=11
we have -1,5,11
now lets see if its AP or GP
if its GP then un=an^(n-1) lets try that out
5=-1*2^(2-1)
5=2 that is wrong And by now you will know its not GP
lets see if its AP then un=a+(n-1)d (d is the difference between the terms here ist 5-(-1)=6)
5=-1+(2-1)6
5=5 hence proved
you can try for the 3rd which will be
11=-1+(3-1)6
11=11
For the next question you asked you should do the same but if you want me to do it i will do it by the way the first term is 1 and the common difference is 4
I hope i helped
and if i did you always free to ask more questions
