Answer:
First equation is -425
Second equation is 11.25
Step-by-step explanation:
First equation we can write as
[tex]\sum_{i=0}^7 5 \times (-2)^i[/tex]
computing
When i=0 -> [tex]5 \times (-2)^0 =5[/tex]
When i=1 -> [tex]5 \times (-2)^1 = -10[/tex]
...
When i=7 -> [tex]5 \times (-2)^7 = --640[/tex]
then replacing each term we have
[tex] 5 + (-10) + ( 20) + ( -40) + (80) +( -160) + 320 + (-640) = -425[/tex]
For the second equation we'll have 9 terms, solving in a similar fashion
When i=1 -> [tex]\frac{1}{4}1=0.25[/tex]
When i=2 -> [tex]\frac{1}{4}2=0.50[/tex]
When i=3 -> [tex]\frac{1}{4}3=0.75[/tex]
...
When i=9 -> [tex]\frac{1}{4}9=2.25[/tex]
So we have 0.25 + 0.50 + 0.75 + 1.00 + 1.25 + 1.50+ 1.75 +2.00 +2.25
