Question

10. Using the following arithmetic sequence, find the 29th term: –36, –32, –28, –24.

Answer 1

–36, –32, –28, –24  This is an arithmetic sequence because each term has the same difference from the preceding term, called the common difference, d...

-32--36=-28--32=-24--28=4  So 4 is d, the common difference.

The sequence of any arithmetic sequence has the form:

a(n)=a+d(n-1), a=first term, d=common difference, n=term number...in this case we have:

a(n)=-36+4(n-1)  

a(n)=-36+4n-4

a(n)=4n-40 so the 29th term is:

a(29)=4(29)-40

a(29)=116-40

a(29)=76

...

distance=velocity * time

d=vt  we want to find t so

t=d/v  and in this case:

t=234/70

t=(210+24)/70

t=3hr+(60*24)/70

t=3hr+20min+34sec so 

t≈3hr 20min

...

This is an arithmetic sequence...100,150,200...

The sum of an arithmetic sequence will always be the average of the first and last terms times the number of terms....

the rule for the sequence is:

a(n)=a+d(n-1),  a(n)=100+50d-50, a(n)=50n+50

Now we know the nth term is 50n+50, and we also know the first term is 100 so:

s(n)=n(100+50n+50)/2  and we want to know the sum of the first 10 terms so

s(10)=10(100+500+50)/2

s(10)=$3250

...

The first two terms are 2 and 4 so:

a(n)=2+2(n-1)

a(n)=2+2n-2

a(n)=2n

a(10)=20

...

You could do synthetic or long division, but you also could just use the fact that the factor being (x+8) should indicate a zero for the function when x=-8.  If f(x) could be divided by (x+8) the value of y(-8) would equal zero, however calculating y(-8)=-10  so that would be the remainder if you did the division.