Question

How come an arithmetic series formula doesn't work when the term is small?

Answer 1

??

Answer 2

it does work

Answer 3

For example,

\[\sum_{i=1}^5{(2)i^2+3}\]

When I write out the sums, I get 5, 11, 21, 35, 53, which add up to 125.

But when I use the formula for arithmetic series, \[S _{n} = (n \div 2)(a_{1}+a_{n}) \] it turns out to be 145? Am I doing something wrong?

Answer 4

Because when I plug in the values for the formula, I get

(5/2)(5+53) = 145

Answer 5

the i squared term means that this isn't an arithmetic sequence/series

Answer 6

if you had 2i + 3 instead, then it would work

Answer 7

Ohhhh ok. Thanks a bunch! I was really confused haha.

Answer 8

you're welcome