Question

What is the sum of the arithmetic sequence 22, 13, 4 … if there are 28 terms? (I want to be explained how to do it, not given the answer)

Answer 1

ok, the first thing to do here is work out the common difference

Answer 2

can you see how to do that?

Answer 3

The common difference is 9 c:

Answer 4

not quite, think of what you need to do to get from 22 to 13? do you add or subtract 9?

Answer 5

subtract 9. So, d = -9.

Answer 6

thats right

Answer 7

so now you know the first term \(a_1\), you know the common difference \(d\) and you know the number of terms \(n\), so just use the formula for the sum as before:\[S_n=\frac{n}{2}(2a_1+(n-1)d)\]

Answer 8

What was the easier version you had before that got me the right answer?

Answer 9

in this case - this formula is the one to use as you know all the terms on the right-hand-side

Answer 10

if you prefer you can also use another method where you first calculate the 28th term using:\[a _{n}=a _{1}+(n-1)d\]

Answer 11

and then calculate the sum of the first 28 terms using:\[S_n=\frac{n}{2}(a_1+a_n)\]

Answer 12

\[28 = 22 (28 - 1)(-9) ?\]

Answer 13

28th term is -221.

Answer 14

no, the formula you are using is supposed to give you the n'th term. so, if you want to calculate the 28'th term, then you would do:\[a_{28}=a_1+(28-1)d\]

Answer 15

remember the \(a_n\) stand for each term in the sequence: \(a_1, a_2, a_3, ..., a_n\)

Answer 16

is the final answer -2,786?

Answer 17

yes :)

Answer 18

Yay :D

Answer 19

:D you will be an expert in these very soon - I'm sure of it! :)