the series has 8 terms. evaluate the series 1/2,3/2,5/2,…,15/2
you

This is an arithmetic sequence, not a series, (series are infinite, sequences are finite) because each term is a constant difference from the term preceding it, called the common difference.

Technically the sum of any arithmetic sequence is:

s(n)=(2an+dn^2-dn)/2

However the above equation is derived from the fact that the sum of an arithmetic sequence is the average of the first and last terms times the number of terms in the sequence.

All we really have to "solve" for then is the number of terms in the sequence...the rule for the sequence of an arithmetic sequence is:

a(n)=a+d(n-1), a=first term, d=common difference, n=term number.  Since we know a=1/2 and d=1 we can solve for n...

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

a(n)=n-1/2, now we just solve for n when a(n)=15/2

15/2=n-1/2

n=16/2

n=8  so there are seven terms, now we can say:

s(8)=8(1/2+15/2)/2

s(8)=32

110698.56 square miles

step-by-step explanation:

multiply 3.8 by 102

387.6

multiply 2.8 by 102

285.6

multiply those two to get

110698.56 square miles