Evaluate the sum.
-$$\sum _ { \mathrm { i } = 4 } ^ { 14 } ( \mathrm { i } + 8 )$$
A) 169
B) 187
C) 173
D) 183

Question

Quizplus · Accepted Answer

The sum can be simplified as follows: $\sum _ { i = 4 } ^ { 14 } ( i + 8 ) = 4 + 8 + 5 + 8 + 6 + 8 + ... + 14 + 8$. This is equivalent to summing the integers from 4 to 14 and then adding 8 eleven times (since there are 11 terms from 4 to 14 inclusive). The sum of an arithmetic series is given by $n/2 \cdot (first\ term + last\ term)$, where $n$ is the number of terms. Here, $n = 14 - 4 + 1 = 11$, so the sum of the integers from 4 to 14 is $11/2 \cdot (4 + 14) = 99$. Adding 8 eleven times gives $8 \cdot 11 = 88$. Adding these two results gives $99 + 88 = 187$.

Evaluate the Sum ∑i=414(i+8)\sum _ { \mathrm { i } = 4 } ^ { 14 } ( \mathrm { i } + 8 )i=4∑14​(i+8)

Evaluate the Sum $\sum _ { \mathrm { i } = 4 } ^ { 14 } ( \mathrm { i } + 8 )$