Let us first closely examine the sequence for any mathematical correlation between the numbers of sequence

It is visualized that sequence, is progressing with multiplication of ×2 in the number of the sequence then addition of increasing consecutive number starting from +1 (viz 1, 2, 3, 4, 5, 6…) in the previous number of the sequence to obtain next number of the sequence.

The given sequence is

1, 3, 8, 19, 42, 89, ___?

Let us see from first number onward

1 × 2 + 1 = 3

3 × 2 + 2 = 8

8 × 2 + 3 = 19

19 × 2 + 4 = 42

42 × 2 + 5 = 89

89 × 2 + 6 = 184

184 × 2 + 7 = 375

375 × 2 + 8 = 758

The extended sequence is

1, 3, 8, 19, 42, 89, 184, 375, 758

Answer the next numbers in the sequence are 184, 375 and 758