Question

Find the sum of the first 20 terms in the arithmetic series 14 + 3 – 8 – ....

Answer 1

The sum of an arithmetic series is dictated by three numbers...
the first term, the last term, and the common difference.

Obviously, the first term is 14, now what's the common difference?
(HINT: The common difference, if you're sure this is an arithmetic series, may be found by subtracting the first term from the second)

Answer 2

Ok so that would give me -11 correct?

Answer 3

Yes. Now to get the last term.
In this case, it's the 20th term.

To get the 20th term, given the first term and the common difference, use this formula.
\[\huge a_n \ = a_1+(n-1)d\\\huge a_{20}=a_1+(20-1)d\]
Where \(a_1\) is the first term and \(d\) is the common difference.

Answer 4

Ok cool, thanks!

Answer 5

That is not yet the answer.
Once you get the nth (20th) term, you are ready to get the sum of the first n (20) terms. Use this formula.
\[\huge S_n \ = \frac{n(a_1+a_n)}{2}\\\huge S_{20}=\frac{20(a_1+a_{20})}{2}=10(a_1+a_{20})\]

Answer 6

okk hold up let me do the first part

Answer 7

how do I do: \[a _{n}=14+(n-1)-11 \]
\[a _{20}=14+(20-1)-11\]

Answer 8

slight correction...\[a _{20}=14+(20-1)\color{red}{(-11)}\]
Things would go horribly wrong if you had added that -11 instead of multiplying it.