Find the value of 6 + 11 + 16 + 21 + 21 + .... + 71.

 

The given sequence is a combination of three series:
i)1st, 4th, 7th terms i.e, 2, 4, 9
ii)2nd, 5th, 8th terms i.e, 3, 6, 12
iii)3rd, 6th, 9th terms i.e, 4, 8, 16
In each one of i, ii, iii, each term is twice the preceding term.
So, 9 is wrong and must be replaced by (4*2) = 8

The correct pattern is *2+1
So, 39 is wrong and must be replaced by (15 * 2 + 1) = 31

The correct pattern is +1, -2, +3, -4, +5, . . . .
So,129 wrong and must be replaced by 123 + 5 = 128

Each term of the series is the product of the preceding two terms
So, 5000 is wrong and it must be replaced by (500*50) = 25000

The correct pattern is +9,-7,+5,-3,+1
So,85 is wrong term and must be replaced by 90-3=87

The correct pattern is +4,+7,+10,+13,+16
So, 36 is wrong term and it must be replaced by 25+13=38

The sequence is 13*13,12*12,11*11,10*10,9*9,8*8, . . . . . .
So,85 is wrong term and must be replaced by 9*81

The given sequence is a combination of two series
1)31,35,39,43,47
2) 45,47,49,51,53
So,the missing term is 49