next number of the sequence 6, 26, 16, 96, 56, 376, ..... will be

+20 , -10(half)
+40,-20
+320,-160

6, 26, 16, 96, 56, 376, .....

Diff in terms ... 20, -10, 80, -40, 320, -160

so next number will be 376-160 = 216 .. option 1

(6+26)/2=16
(16+96)/2=56
(56+376)/2=216

16-6=10
56-16=40
x-56=160
then x=56+160
x=216

The given sequence is formed by two sequences.
Where odd number form one sequence, even number form another sequence with same difference.

6, 16, 56, .... odd number sequence.
and 26, 96, 376... even number sequence.

Let 6 (last digit) be fix as all number end with 6. (This may not be applicable for all sequences) and denote it as Y...

Consider remaining digits except Y (6, last digit) as X... each time X is incremented by
---> (X*4)+1

and sequence is formed as XY... (not a multiplication)

So after 56 next number will be (5 * 4)+1 = 21

Answer will be ---> 216....

26*6=156
if three didit remove middle no.=16.
:16*6=96.
:96*6=576 =56
:56*6=336 =36
:36*6=216

6,26,16,96,56,376....
26-6=20
16-26=-10
96-16=80
56-96=-40
376-56=320
next term will be
376-4*-40=216

Initally consider n=2; m=n/2;
6 = 6
6 + n = 26 (6+20)
26 - m = 16 (26-10)
16 + (n*4) = 96 (16+80)
96 - (m*4) = 56 (96-40) -----------(n=80;m=n/2)
56 + (n*4) = 376 (56+320)
376- (m*4) = 216 (376-160)----------(n=320;m=n/2)

2nd number is increased by 20 from the previous number, 3rd is reduced by 10 from the previous number (half of the previous number).

26-6=20
20/2=10,next number is 26-10=16
96-16=80,80/2=40
next number is 96-40=56,
so 376-56=320,320/2=160
next number is 376-160=216

adding x and subtracting x/2

16-6=10
56-16=40
40*4=160
160+56=216

according to series +20-10+80-40+320-160...acc to calculation this is the answer

difference 20,-10,80,-40,320,-160

16-6=10
56-16=40
x-56=160
x=216

16-6=10
56-16=40
216-56=160

6 26 16 96 56 376
6+20=26 6+10=16
16+80=96 16+40=56

56+320=376 so 56+160=216

There are two number sequence involved:
6, 16, 56, ... (differences: 10, 40 (10*4), 160 (40 *4))
26, 96, 376 ... (Differences: 70, 280 (70*4))

Hence next number in the sequence will be: 56 + 160 = 216
Ans: option 1

There are two alternate series as 6,16,56,..... and 26,96,376......
next term in each series is find by subtracting 2 from the term and then multiplying by 4 as shown below:

(6-2)*4 = 16,(16-2)*4 = 56,(56-2)*4 = 216

(26-2)*4 = 96,(96-2)*4 = 376