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