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

Question

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with the first term 7 and a common difference of 6. The term $6k + 1$ is the k-th term. For $P_{k+1}$, the next term is $[6(k+1) + 1]$, which simplifies to $[6k + 7]$. Thus, $P_{k+1}$ includes all terms up to $[6k + 1]$ and adds the next term $[6(k+1) + 1]$.

Find Pk+1P _ { k + 1 }Pk+1​ For the Given PkP _ { k }Pk​

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