Question

@amistre64

Answer 1

wht do we know about the sum of an arithmetic series?

Answer 2

It's the sum of an arithmetic sequence.

Answer 3

yeah, for demonstration:

is 1,2,3,4,5 an arithmetic sequence?

Answer 4

Nooo it's a progression

Answer 5

its a sequence of numbers, a progression of numbers, the is 1 more than the one before it ....

Answer 6

its arithmatic

Answer 7

Yes common difference 1

Answer 8

so lets use this simple thing to work out how to solve the sum of the term

S = 1 + 2 + 3 + 4 + 5
+S = 5 + 4 + 3 + 2 + 1
---------------------
2S = 6 + 6 + 6 + 6 + 6

does this make sense? we simply double the sum by flipping it around and adding them together

Answer 9

that double what the sum is

and this is just an example

notice that the first term (1) plus the last term (5) is equal to (6) which is the sum of all our individual parts

Answer 10

n terms, of (first + last) is 2 times greater than the sum of the series.

\[2S=n(first+last)\]
\[S=\frac{n}{2}(first+last)\]
we know all these parts

Answer 11

Okay now what?

Answer 12

now we use this knowledge to find the answer of course.

Answer 13

Okay so can you walk me through each step please?

Answer 14

what is our first term?

what is our last term?

how many terms are in the sequence?

Answer 15

1st term is 1, last term is 154?

Answer 16

good so far, and number of terms?

Answer 17

52?

Answer 18

correct so all we do is fill in the parts

\[S=\frac{n}{2}(first+last)\]
\[S=\frac{52}{2}(1+154)\]

Answer 19

S=26(1+54)
S=26(1404)
S=36504

Answer 20

i think your fingers got twisted ...

S = 26(155)

Answer 21

Oops lol 4030.

Answer 22

thats better :)

Answer 23

Help me with another one? I want to make sure I get it right.

Answer 24

1 more

Answer 25

Okay.