Series Completion

+1, +1, +2, +2, +3

The series is: 2²=4, 4²=16, 6²=36, 8²=64. These are squares of consecutive even numbers. The next even number is 10, and 10²=100.

+10,-20,+10,-20,+10

ans=21

ADD n^2 + n for nth no.

pattern is - /5,/4,/3,/2....
so,ans=7/1=7

5,   ,52,      ,522,          ,5222
   2   ,     22,          222                2222

PATTERN IS-*2+1,*2-1,*2+1,2-1
372+1=75

*8,*4,2
SO, 1282=256

11-1,22-2,33-1,44-2

The pattern follows decreasing subtractions: 66-30=36, 36-18=18, 18-10=8. The amounts subtracted (30, 18, 10) decrease by 12, then 8, then 4 - each reduction is half of the previous reduction. This gives the next term as 8, though the pattern is complex and not immediately obvious.

+7,+7

BACBACBACBAC

*2,*3,*4,*5

*2,*1,*2,*1

Add the digits to get the next number.

+5,+4,+3,+2

21,21-11,21-22,21-33,21-44

Option (3) is the odd one out as the letters are not consecutive letters of the English alphabet.

+30,+60,+90,+120
345+120=465

Add the sum of the digits to the number itself to get the next number.

 40 + (5-2) = 43
 22 + (2-1) = 23 
 21 + (1-x) = 20
 => x = 2

Add 111

ADD PRIME NO. TO GET NEXT NO.
+2, +3, +5, +7, +11
19 + 11 = 30

*3, *3, *3

*4, -2, *4, -2, *4, -2
22 * 4 = 88