SOLUTION: How many terms of the series 5+9+13+17... Must be added so that the sum will be 230? Please show the solution

First we find the common difference by subtracting
consecutive terms:

9-5=4
13-9=4
17-13=4

So the common difference d=4

Then we learn the formula for the sum of the first
n terms:



and learn what the terms mean:

n = the number of terms
Sn = the sum of the first n terms
a1 = the first term
d = the common difference

We substitute Sn=230, a1=5, and d=4
in 



and get



Multiply 2*5 and get 10



Move the 4 in front of the (n-1)



Distribute the 4 into the (n-1)



Combine the 10 and the -4 getting 6 



Clear the fraction by multiplying both sides by 2:



Multiply the 2 times the 230 on the left getting 460.
Cancel the 2's on the right:



Now we have:



Can you solve that for n?  If not ask me how in the thank-you
note form below and I'll get back to you by email.

Edwin