1, 2, 5, 12, 27, 58, 121, ?

Answer: Option C

Explanation:

\begin{aligned}
\text{Pattern is }\\
+1^2-1, +2^2-1, +3^2-1,+4^2-1 \\
5^2-1 = 28 + 24 \\
= 52
\end{aligned}

Answer: Option A

Explanation:

Pattern in the series is, -2, -4, -2, -4. So next term will be -2
24 -2 = 22

Answer: Option B

Explanation:

Pattern in the series is, +20.5 , +22.5,
Next will be +24.5
138 + 24.5 = 162.5

Answer: Option B

Explanation:

Please check, given sequence is combination of two seies
[Note: Usually when terms are more than 5, then chances are there that it may contain 2 series.]

Series 1 = 11, 17, 23
Series 2 = 12, 18, 24

So there is pattern +6 in each term
Next term will be 23+6 = 29

Answer: Option B

Explanation:

Pattern is +5, +10, + 15, +20

Next number in the series will be 56 + 25 = 81