MATH SOLVE

2 months ago

Q:
# 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

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