Find $P _ { k + 1 }$ For the Given $P _ { k }$

Find $P _ { k + 1 }$ for the given $P _ { k }$ .
$$P _ { k } = 7 + 13 + 19 + \ldots + [ 6 ( k - 1 ) + 1 ] + [ 6 k + 1 ]$$

A) $P _ { k + 1 } = 7 + 13 + 19 + \ldots + [ 6 k + 7 ] + [ 6 ( k + 1 ) + 1 ]$
B) $P _ { k + 1 } = 7 + 13 + 19 + \ldots + [ 6 k + 1 ] + [ 6 ( k + 1 ) + 7 ]$
C) $P _ { k + 1 } = 7 + 13 + 19 + \ldots + [ 6 k + 7 ] + [ 6 ( k + 1 ) + 7 ]$
D) $P _ { k + 1 } = 7 + 13 + 19 + \ldots + [ 6 k + 1 ] + [ 6 ( k + 1 ) + 1 ]$
E) $\quad P _ { k + 1 } = 7 + 13 + 19 + \ldots + [ 6 ( k - 1 ) + 1 ] + [ 6 k + 1 ]$

Correct Answer:

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