math

thats right and we will leave it at that because it is far to complicated to explain otherwise.

Originally posted by sonhouse
I got 1050. I did it in groups of 5, 18+20+22+24+26 and found each group starting with 110 sum going up by 50 so it was easy to truncate the series, 110+160+210+260+310= 1050

There is an easier way to do this. Just sum the first integer with the last. You get 12 pairs with equal sums, count them all together and add the one integer that was left as the number of integers given is odd.

For example 1+2+3+...+99+100+101=50*((1+101)+(2+100)+...+(50+52))+51=5151

the way we had to do it on my final was as follows :

An = A1 + (n-1)d

where
An = any term
A1 = first term
n = number of terms in the sequence
d = arithmatic difference between terms

so

An = 18 + (25-1)2
An = 18 + 48
An = 66 < last term in the sequence

then find the sum using the sum formula for any arithmatic sequence

Sn = (n/2) (A1 + An)

where
Sn = sum
n = number of terms in sequence
A1 = first term
An = last term

so

Sn = (25/2) (18 + 66)
Sn = 25 ( 9 + 33)
Sn = 25 ( 42 )
Sn = 1050

Originally posted by Drew L
the way we had to do it on my final was as follows :

An = A1 + (n-1)d

where
An = any term
A1 = first term
n = number of terms in the sequence
d = arithmatic difference between terms

so

An = 18 + (25-1)2
An = 18 + 48
An = 66 < last term in the sequence

then find the sum using the sum formula for any arithmatic sequence

Sn = (n/2) ( ...[text shortened]... rm
An = last term

so

Sn = (25/2) (18 + 66)
Sn = 25 ( 9 + 33)
Sn = 25 ( 42 )
Sn = 1050

Yeah that is another way to do so. But the way I described was used by Karl Gauss when he was a kid. For behaving, he was asked by his teacher to sum all natural numbers from 1 to 100. Surprisingly, he had the answer in a matter of seconds, and the way I described it is how he did it. Of course they way you describe is taught in school and I've learned it as well and I think both ways are good enough.

Originally posted by kbaumen
Yeah that is another way to do so. But the way I described was used by Karl Gauss when he was a kid. For behaving, he was asked by his teacher to sum all natural numbers from 1 to 100. Surprisingly, he had the answer in a matter of seconds, and the way I described it is how he did it. Of course they way you describe is taught in school and I've learned it as well and I think both ways are good enough.

Wow, what did those kids have to do if they started acting up or something? 🙂