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