Question

What number is needed to complete the pattern below 66 73 13 21 52 _1020

Answer 1

we have

$66,73, 13, 21, 52, x, 10, 20$

let

$a1=66,a2=73,a3=13,a4=21,a5=52,a6=x,a7=10,a8=20$

we know that

$a2-a1=73-66\\ a2-a1=7\\ a2=a1+7$

$a4-a3=21-13\\ a4-a3=8\\ a4=a3+8$

$a6-a5=x-52\\ a6=a5+(x-52)$

$a8-a7=20-10\\ a8-a7=10\\ a8=a7+10$

Basing on this pattern the term $(x-52)$ should be $9$

$x-52=9\\ x=9+52\\ x=61$

therefore

the answer is

the number needed to complete the pattern is $61$

Answer 2

The answer is 61. First is knowing the pattern. By subtracting the second number with the first then fourth number with the fifth and so on, you get.

73 minus 66 equals 7.
21 minus 13 equals 8.
xx minus 52 equals x.
20 minus 10 equals 10.

Basing on this pattern x should be 9 and you get the number xx by adding 52 and 9 which is 61.