Q1. 5, 10, 17, 26, 39, 50, 65
To the first term 5 is added to get the second
To the second term 7 is added to get the third
To the third term 9 is added to get the fourth
Continuing this sequence 11 must be added to get the fifth term.
Hence fifth term is 26+11 = 37 and not 38.
Now adding 13 to 37 gives 50 and adding 15 to 50 gives 65.
Hence in the above sequence 5,7,9,11,13,15 are respectively added to the previous terms to get the next term in the sequence.
Q 2 : 3 , 5 , 7 , 11 , 13 , 17 , 21
All the terms are prime numbers other than 21. It must be 19 and not 21
Q 3 : 2 , 9 , 17 , 65 , 126 , 217 , 344
If you observe the sequence it is of the form 
i.e; 
Hence the third term must be 28 and not 17.
Q 4 : 4 , 25 , 100 , 289 , 652 , 1369 , 2500
The sequence above is of the form
To the base of each number 3, 5 , 7, 9, 11, 13 are added
Hence the fifth term must be
and not 652.
Regards,
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