What is the sum of all positive odd multiples of 3 that are less than 100?

Question

Can someone explain this to me please. I have no idea if my daughter has the right answer.

Answer 1

First determine the series:

3 + 9 + 15 + 21...Note the number increase by 6.

a_n > 3 + (n - 1)6

100 > 3 + 6n - 6

100 > -3 + 6n

103 > 6n

17.16 > n

99 = a₁₇

S₁₇ = (17/2)(3 + 99)

S₁₇ = (17/2)(102)

S₁₇ = (17)(51)

S₁₇= 867

 

Answer 2

odd multiples of 3 that are less than 100 are

3, 9, 15, 21, 27, 33, 39, and 45,51,57,63,69,75,81,87,93,99

add all these to get answer