Question

The value of ${\sum }_{k=1}^{16}(2k-3)$ is _______.

• A. 390
• B. 195
• C. 210
• D. None of these

Answer 1

The correct option is D None of these

Distribute the $\sum$ over the terms ,

${\sum }_{k=1}^{16}(2k-3)={\sum }_{k=1}^{16}2k-{\sum }_{k=1}^{16}3$

$\Rightarrow$ ${\sum }_{k=1}^{16}(2k-3)=2{\sum }_{k=1}^{16}k-3{\sum }_{k=1}^{16}$

$=2\times \frac{n(n+1)}{2}-3\times \left(n\right)$ where $n=16$

$=2\times \frac{16\times 17}{2}-3\times 16$

$=272-48$

$=224$