Find the indicated partial sum for the sequence with the given general term.
-s $5 , a _ { n } = 5 n - 11$
A) $- 30$
B) 14
C) $- 6$
D) 20

Question

Quizplus · Accepted Answer

To find the partial sum, we need to use the formula:
$$S_n=\sum_{i=1}^{n}a_i$$
where $S_n$ is the $n$th partial sum and $a_i$ is the $i$th term of the sequence.

Substituting the given general term, we get:
$$S_n=\sum_{i=1}^{n}(5i-11)$$

Now we can use the formula for the sum of an arithmetic sequence:
$$\sum_{i=1}^{n}i=\frac{n(n+1)}{2}$$

Substituting this, we get:
$$S_n=\frac{5n(n+1)}{2}-11n$$

To find the indicated partial sum, we need to substitute $n=5$:
$$S_5=\frac{5(5+1)}{2}(5)-11(5)=50$$

Therefore, the best choice is D, with a partial sum of 20.

Find the Indicated Partial Sum for the Sequence with the Given