Answer
a. $-\frac{1}{2}$
b. $31$
c. $13$
d. $0$
Work Step by Step
Given $\Sigma_{k=1}^{10} a_k=-2$ and $\Sigma_{k=1}^{10} b_k=25$, we have:
a. $\Sigma_{k=1}^{10} \frac{a_k}{4}=\frac{1}{4}\Sigma_{k=1}^{10} a_k=-\frac{1}{2}$
b. $\Sigma_{k=1}^{10} (b_k-3a_k)=\Sigma_{k=1}^{10} b_k-3\Sigma_{k=1}^{10} a_k=25-3(-2)=31$
c. $\Sigma_{k=1}^{10} (a_k+b_k-1)=\Sigma_{k=1}^{10} a_k+\Sigma_{k=1}^{10} b_k-\Sigma_{k=1}^{10} 1=(-2)+25-10=13$
d. $\Sigma_{k=1}^{10} (\frac{5}{2}-b_k)=\Sigma_{k=1}^{10} \frac{5}{2}-\Sigma_{k=1}^{10} b_k=\frac{5}{2}\times10-25=0$
