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The given series having following pattern:

  • $3*1+2=3$
  • $5*2+2=12$
  • $12*3+2=38 \rightarrow (39)$ is wrong term here.
  • $38*4+2=154$
  • $154*5+2=772$
  • $772*6+2=4634$

$\therefore$ Option $(C)$ is correct here.

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