The first 100 counting numbers are arrangedin columns as shown. What would be the sum of all numbers in column c?

Question

Set up like this

 

A     B     C     D     E

1     2     3     4     5

10   9     8     7     6

11   12   13   14   15

20   19   18   17   16

 

we have answer of 968 but we wrote it all out the long way, is there a formula you could do we know the pattern in the column is add 5 each time?

Answer 1

Yes there is a formula for the sum of an arithmetic series. S_n = n(a₁ + a_n)/2

 

Where S_n is the sum, n is the number of terms, a₁ is the first term, and a_n is the last term.

 

Plugging in we get S_n = 20(3 + 98)/2

 

S_n = 1010

Answer 2

There are two arithmetic series:

4, 14, 24, 34, ... and

7, 17, 27, 37, ...

For the top

S₁₀ = (10/2)(2(4) + 9(10)), or 490

For the bottom

S₁₀ = (10/2)(2(7) + 9(10)), or 520

The sum of the two is 1,010