Question

Write the related series for each finite sequence the. Evaluate the series. For problems 2,4,6. Thank you.

Answer 1

To evaluate the series we proceed as follows:
2. -5,-15,-25,-35,-45
The common difference is (-15--5)=-10
thus the series is an arithmetic sequence hence the explicit formula will be:
an=a+(n-1)d
thus the formula for the series is:
an=-5+(n-1)(-10)
an=-10n+5

4. 0.5, 0.25,0,...,-0.75
The common difference =0.25-0.5=-0.25
The sequence is an arithmetic sequence:
the explicit formula will be:
an=0.5-0.25(n-1)
an=-0.25n+0.75
thus
n=4
a4=-0.25*4+0.75=-0.25
when n=5
a5=-0.25*5+0.75=-0.5
when n=6
a6=-0.25*6+0.75=-0.75
the missing values are -0.25 and -0.5

6] 4.5,5.6,6.7, ....,11.1
common difference=5.6-4.5=1.1
the sequence is an arithmetic sequence
The explicit formula is:
an=4.5+1.1(n-1)
an=1.1n+3.4
when n=4
an=1.1*4+3.4
a4=7.8

when n=5
a5=1.1*5+3.4
a5=8.9

a6=1.1*6+3.4
a6=10
the missing values are: 7.8, 8.9, 10