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1st blank options : +6, +1, +7, +13
2nd blank options: 7,13, 6, 1
3rd blank options: +6 , -1 , +7 , +1
4th blank options: 71 ,59, 69, 61

1st blank: each term is 6 more than the previous one, so the appropriate choice is "+6"

2nd blank: The way we write the generic term of an arithmetic sequence is
  a[n] = a[1] +d*(n -1)
You have a[1] = 7 and d = 6, so this is
  a[n] = 7 +6*(n -1) = 6 +6n -6 = 6n +1
The appropriate choice for the 2nd blank is "6"

3rd blank: see the discussion for the 2nd blank. The appropriate choice is "+1"

4th blank: a[10] = 6*10 +1 = 61. The appropriate choice is "61"

Distributive property