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The sum of the first n terms of 1 + 3 + 5 + 7 + 9 + .. is 144.  Find n.

 Jan 28, 2021
 #1
avatar+52 
+6

I don't want to say that you should necessarily do it this way, but 1+3+5+7+9+11+13+15+17+19+21+23=144 so 12

 Jan 28, 2021
 #2
avatar+377 
+1

A cool pattern is that it's the square, so the first n terms is n^2. 

sqrt(144) = 12

So 12 = n. 

 

:))

=^._.^=

catmg  Jan 28, 2021
 #3
avatar+52 
+5

cool! I didn't know that, thanks :)

mimi997  Jan 28, 2021
 #4
avatar+377 
+1

I love your profile picture. 

It's really pretty. 

 

=^._.^=

catmg  Jan 28, 2021
 #5
avatar+8456 
0

Notice a pattern on the partial sums:

 

1 = 1 = 1^2

1 + 3  = 4 = 2^2

1 + 3 + 5 = 9 = 3^2

1 + 3 + 5 + 7 = 16 = 4^2

 

The sum is equal to n^2, where n is the number of terms. (This can be proven by mathematical induction.)

 

Now, 144 = 12^2. This means n^2 = 12^2, n = 12.

 Jan 28, 2021
 #6
avatar+267 
+1

this is a perfect square pattern. so all we need to find is sqrt144=12 so n=12

 Jan 28, 2021
edited by KitSoundwave  Jan 28, 2021

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