Use the properties of summation and Theorem 5.2 to evaluate the sum. $$\sum _ { i = 1 } ^ { 23 } ( 2 i + 5 )$$
A) 667
B) 552
C) 575
D) 1311
E) 391

Question

Quizplus · Accepted Answer

The sum can be split into two separate sums: $\sum _ { i = 1 } ^ { 23 } 2i + \sum _ { i = 1 } ^ { 23 } 5$. The first sum is an arithmetic series with a common difference of 2, and the second sum is a constant series. The sum of the first series is $2 \times \frac{23(23 + 1)}{2} = 23 \times 24$, and the sum of the second series is $5 \times 23$. Therefore, the total sum is $23 \times 24 + 5 \times 23 = 552 + 115 = 667$.

Use the Properties of Summation and Theorem 5 ∑i=123(2i+5)\sum _ { i = 1 } ^ { 23 } ( 2 i + 5 )i=1∑23​(2i+5)

Use the Properties of Summation and Theorem 5 $\sum _ { i = 1 } ^ { 23 } ( 2 i + 5 )$