The sum of the arithmentic series is -127
Step - by - Step Explanation
What to find? The sum of the arithmetic series.
Parameter Given:
a₁ = -26/5 , d=-5/3 , n=10
To find the sum of the arithmetic series we will use the formula below:
[tex]S=\frac{n}{2}\mleft\lbrace2a+(n-1)d\mright\rbrace[/tex]
Substitute the values and evaluate.
[tex]S=\frac{10}{2}\mleft\lbrace2(\frac{-26}{5}_{})+(10-1)(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace2(\frac{-26}{5})+9(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace-\frac{52}{5}-15\mright\rbrace[/tex][tex]=-52-75[/tex]
=-127
