Posted by **Jill** on Sunday, December 20, 2009 at 5:15pm.

Suppose the singers true love gave presents for n days instead of 12 days what would the toatl number of gifts given on the nth day be?she told us that the sum of consecutive integers from 1 to n is n(n+1) over 2

Someone told me n= 12 and the sum is = to 78. Why?

- algebra -
**Damon**, Sunday, December 20, 2009 at 5:49pm
G(n) = 1 + 2 + 3 + 4 + 5 + ....n

to get the average of that sequence add the first and the last and divide by 2

for example

1 + 2 + 3 + 4 + 5 + 6 = 1+6 + 2+5 + 3+4

= 7 + 7 + 7

the average is 7 which is 1+6 divided by 2 (or 2+5 divided by 2 or 3+4 divided by 2

)

then multiply the average (1/2)(n+1)

by the number of terms, n, to get the total.

So yes, your formula is right.

1 + 2 + .... 12

= (1/2)(1+12)(12)

=13*6

= 78 sure enough

- algebra -
**Damon**, Sunday, December 20, 2009 at 6:07pm
I explained that poorly:

G(n) = 1 + 2 + 3 + 4 + 5 + ....n

to get the sums of that sequence add the first and the last and the second and the second to last etc. in pairs

1 + 2 + 3 + 4 + 5 + 6 = 1+6 + 2+5 + 3+4

= 7 + 7 + 7

each sum is 7 which is 1+6 divided by 2 (or 2+5 divided by 2 or 3+4 divided by 2

)

and there are n/2 of those pairs

So yes, your formula is right.

1 + 2 + .... 12

= (1/2)(1+12)(12)

=13*6

= 78 sure enough

- algebra -
**Damon**, Sunday, December 20, 2009 at 6:09pm
aaarrgggh another mistake

G(n) = 1 + 2 + 3 + 4 + 5 + ....n

to get the sums of that sequence add the first and the last and the second and the second to last etc. in pairs

1 + 2 + 3 + 4 + 5 + 6 = 1+6 + 2+5 + 3+4

= 7 + 7 + 7

each sum is 7 which is 1+6 (or 2+5 or 3+4 )

and there are n/2 of those pairs

So yes, your formula is right.

1 + 2 + .... 12

= (1/2)(1+12)(12)

=13*6

= 78 sure enough

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