Pattern: $\div 4$. $1536/4=384$ should be there, 386 is wrong.

Pattern is based on cubes of differences: $1^3=1, 2^3=8, 3^3=27, 4^3=64, 5^3=125$. Series: $1+1^3=2, 2+2^3=10, 10+3^3=37, 37+4^3=101, 101+5^3=226$.

Logic: The series is in the form $(n^3-n)$. $3^3-3=24$, $4^3-4=60$, $5^3-5=120$, $6^3-6=210$, $7^3-7=336$.

Pattern: $5\times 1-1 = 4$, $4\times 2-2 = 6$, $6\times 3-3 = 15$, $15\times 4-4 = 56$, $56\times 5-5 = 275$.

Pattern: $1\times 1+1^2 = 2$, $2\times 2+2^2 = 8$, $8\times 3+3^2 = 33$, $33\times 4+4^2 = 148$, $148\times 5+5^2 = 740+25 = 765$.

It is a mixed series: I: $4, 16, 36, 64 \rightarrow 2^2, 4^2, 6^2, 8^2$. II: $196, 144, 100, ? \rightarrow 14^2, 12^2, 10^2, 8^2=64$.

Logic: $2 \times 1 + 1 = 3$, $3 \times 2 + 2 = 8$, $8 \times 3 + 3 = 27$, $27 \times 4 + 4 = 112$, $112 \times 5 + 5 = 565$.

Pattern: $(2^3-1)=7$, $(3^3-1)=26$, $(4^3-1)=63$, $(5^3-1)=124$, $(6^3-1)=215$. Thus, $(7^3-1)=343-1=342$.

Pattern: $1^3 + 3 = 4$, $2^3 + 3 = 11$, $3^3 + 3 = 30$, $4^3 + 3 = 67$, $5^3 + 3 = 128$. Thus, $6^3 + 3 = 216 + 3 = 219$.

Pattern: +3, +2, +1... 4, 7, 9, 10, 13, 15, 16, 19. Both correct.

Pattern: $\frac{20}{2} + 2 = 12$, $\frac{12}{2} + 4 = 10$, $\frac{10}{2} + 8 = 13$, $\frac{13}{2} + 16 = 6.5 + 16 = 22.5$.

Each term is the product of the preceding two terms. $2 \times 5=10, 5 \times 10=50, 10 \times 50=500, 50 \times 500=25000$ (not 5000).

This is an arithmetic progression where $a=5, d=8-5=3, T_n=320$. $T_n = a+(n-1)d \Rightarrow 320 = 5+(n-1)3 \Rightarrow 315 = (n-1)3 \Rightarrow 105 = n-1 \Rightarrow n=106$.

Pattern: Sum of squares. $1^2+2^2+3^2+4^2+5^2+6^2=91$. The question might have an error in options or expected output.

Logic: $2 \times 4 - 1 = 7$, $7 \times 4 - 1 = 27$, $27 \times 4 - 1 = 107$, $107 \times 4 - 1 = 427$, $427 \times 4 - 1 = 1707$.

Pattern: +1, +3, +5, +7, +9. $17+9=26$ should be there, 28 is wrong.

It is an arithmetic progression. First term (a) = 10, common difference (d) = 7. $T_n = a+(n-1)d$. For option (B): $346 = 10 + (n-1)7 \Rightarrow 343 = (n-1)7 \Rightarrow 49 = n-1 \Rightarrow n = 50$. Since n is an integer, 346 is a term of the series.

Differences: +5, +8, +11, +14, +17, +20. $32+14=46$ should be there, 47 is wrong.

Differences: +3, +5, +7, +9, +11, +13, +15. $50+15=65$ should be there, 64 is wrong.

Pattern: $1^2 \times 2 = 2$, $2^2 \times 2 = 8$, $3^2 \times 2 = 18$, $4^2 \times 2 = 32$, $5^2 \times 2 = 50$. Thus, $6^2 \times 2 = 36 \times 2 = 72$.