Sum of odd integers greater than 15 but less than 241

[whitehorsey]

1. Find the sum of the odd integers greater than 15 but less than 241.
a. 14,336
b. 28,672
c. 14,448
d. 28896



2. a_n = a₁ + (n-1)*d



3. I know that n = 8 and a₁= 17 and d = 2. But I don't know how to get one of these answers:
14,336
28,672
14,448
28896

 

[Dick]

It's an arithmetic progression. Look it up. Or try adding (17+19+...+237+239) to (239+237+...+19+17) term by term and draw your own conclusions.

 

[HallsofIvy]

One way to find a sum of numbers is to find their average value of the numbers, then multiply by how many numbers there are.

A very nice property of arithmetic progressions is that the average of all the numbers in the progression is the same as the average of the first and last numbers only. What is the first number in this progression? What is the last? What is their average? How many numbers are there?

 

[chriscolose]

If you have been introduced to sigma (summation) notation you can also write the progression of odd numbers as,

$$\sum2n+1$$

where the sum ranges from 8 to 119. Same idea really. You have a basic formula for the arithmetic progression, which HalllsofIvy gave you in words.