Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
-$11 + 14 + 17 + 20 + \ldots + 35$
A) $\sum _ { \mathrm { k } = 2 } ^ { 10 } 3 \mathrm { k } + 5$
B) $\sum _ { k = 0 } ^ { 24 } 3 k + 5$
C) $\sum _ { \mathrm { k } = 1 } ^ { 10 } 3 \mathrm { k } + 5$
D) $\sum _ { k = 2 } ^ { 24 } 3 k + 5$

Question

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with a common difference of 3, starting from 11. The nth term of an arithmetic sequence can be expressed as $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. For the given sequence, $a_1 = 11$ and $d = 3$, so $a_n = 11 + (n - 1)3 = 3n + 8$. Adjusting to match the options, we can rewrite $3n + 8$ as $3(n+2) + 5$, which matches the form in option A when considering the sequence starts at 11 (which corresponds to $k=2$ in the summation) and ends at 35. To find the upper limit of the summation, we solve $3k + 8 = 35$ for $k$, giving $k = 9$. Adjusting for the index starting at 2, the upper limit becomes 10.

Express the Sum Using Summation Notation 11+14+17+20+…+3511 + 14 + 17 + 20 + \ldots + 3511+14+17+20+…+35

Express the Sum Using Summation Notation $11 + 14 + 17 + 20 + \ldots + 35$