If the sum of the arithmetic series #7 + 9 + 11 + 13 + 15 + . . .# is #25,613,712#, then how many terms were added up?

1 Answer
George C.
Mar 10, 2018

#5058#

Explanation:

Note that the sum of the first #n# odd numbers is #n^2#

So, writing #n# for the number of terms we are looking for:

#9+25613712 = (1+3+5)+(7+9+11+...+(2(n+3)-1))#

#color(white)(9+25613712) = (n+3)^2#

So:

#n = sqrt(9+25613712)-3 =5058#

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