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So,
a+(k-1)d= a/(1-d)
solving we have, a=(k-1)* (1-d)
now we look at options:
for d=1/3 -> (1-d)=2/3
since (k-1) and ' a ' both are integers so a=(k-1)*2/3
so k-1 should be divisible by 3 and the product is multiplied by 2 to get ' a '
so 'a' is a multiple of 2 and since it is given that 'a' is prime and greater than 2 so its not possible
similar is the case with d=1/5 or d=1/9
only option left is d=1/2
1-d=1/2
so a=(k-1)* 1/2
if k=7 we get a=3 which is prime
or if k=15 ,a=7 which is prime
so we can get infinite prime a's for d=1/2
and no prime a>2 for other options
so answer is d=1/2
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