Evaluate the sum. $$\sum _ { k = 2 } ^ { 5 } 2 k$$
A) 2
B) 56
C) 28
D) 5
E) none of these

Question

Quizplus · Accepted Answer

We use the formula for the sum of an arithmetic series:
$S_n = \frac{n}{2}(a_1 + a_n)$
where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, and $a_n$ is the $n$th term. In this case, $n=4$, $a_1=4$, and $a_n=10$, so
$$\sum_{k=2}^5 2k = 2\cdot 2 + 2\cdot 3 + 2\cdot 4 + 2\cdot 5 = 4+6+8+10 = 28 = S_4$$
Therefore, the answer is $\boxed{\text{(C)}}$.

Evaluate the Sum ∑k=252k\sum _ { k = 2 } ^ { 5 } 2 kk=2∑5​2k

Evaluate the Sum $\sum _ { k = 2 } ^ { 5 } 2 k$