What is the sum of the first 35 terms in the series 7 + 9 + 11 + ... ?

a.

29

c.

1645

b.

1399

d.

1435

If a sequence is arithmetic or geometric there are formulas to find the sum of the first nn terms, denoted Sn, without actually adding all of the terms.

(Note that a sequence can be neither arithmetic nor geometric, in which case you'll need to add using brute force, or some other strategy.)

To find the sum of the first nn terms of an arithmetic sequence use the formula, Sn=[n (a1+an) ]/2

where n is the number of terms, a1 is the first term and an is the last term.

First find the 35 th term:

a35=a1 + (n-1) (d) = 7 + (34) (2) = 75

Then find the sum:

Sn=[n (a1+an) ]/2 = [35 (7+75) ]/2 = 1435

Thus, the answer is:

d.

1435