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

 

one of the letter from beginning and one of the letter from the end of a term are removed, one by one, alternate steps

The given sequence is a combination of two series:
i.)Y,T, O and ii.)B, G, ?
i. consists of 2nd, 7th, 12th letters from end of English alphabet,while
ii. consists of 2nd, 7th, 12th letters from beginning of English alphabet
So, the missing letter in ii.) is the 12th letter from the beginning of English alphabet,which is L.

Z - 2 = X
X - 5 = S
S - 10 = I
I - 17 = R
R - 26 = R
R - 37 = G
G - 50 = I
The series 2, 5, 10, 17, 26, 37, 50 is obtained by the pattern +3, +5, +7, +9, . . . .

T - 2 = R
R - 2 = P
P - 2 = N
N - 2 = L
L - 2 = J
J - 2 = H

The given sequence is a combination of two series:
i)0, 3, 8, 15, 24, 35
ii)2, 5, 10, 18, 26
The pattern in both i, ii is +3, +5, +7, . . . .
So, in ii) 18 is wrong and must be replaced by (10 + 7) = 17

The correct pattern is -192, -96, -48, -24, -12, -6
So, 48 is wrong and must be replaced by (92 - 48) = 44

The terms of the given series is 1*1, 2*2 + 1, 3*3, 4*4 +1, 5*5, 6*6 + 1, . . . . .
So, 15 is wrong and must be replaced by (4*4 + 1) = 17

The correct pattern is *1+1, *2+2, *3+3, *4+4, . . . . .
So,32 is wrong term and must be replaced by (10 * 3 + 3) = 33