Answer:
345
Step-by-step explanation:
We know that [tex]1+2+3+...+n=\frac{n(n+1)}{2}[/tex]
Given pattern : [tex]-1 + 2 + 5 + 8 + ... + 44[/tex]
-1 + 2 + 5 + 8 + ... + 44 = \sum_{i=0}^{15} 3x-1
We can write [tex]\sum_{i=0}^{15} 3x-1=3\sum_{i=0}^{15}x-\sum_{i=0}^{15}1[/tex]
Here, [tex]3\sum_{i=0}^{15}x=3\left ( 1+2+3+...+15 \right )[/tex]
On putting n = 15 in [tex]\frac{15(15+1)}{2}=\frac{15\times 16}{2}=120[/tex]
So, [tex]3\sum_{i=0}^{15}x=3(120)=360[/tex]
Also, [tex]\sum_{i=0}^{15}1=15[/tex]
Therefore,
[tex]-1 + 2 + 5 + 8 + ... + 44\\=\sum_{i=0}^{15} \left ( 3x-1 \right )\\=3\sum_{i=0}^{15}x-\sum_{i=0}^{15}1\\=3\left ( 0+1+2+3+...+15 \right )-15\\=3\left [ \frac{15\left ( 15+1 \right )}{2} \right ]-15\\=360-15\\=345[/tex]
