Question

Find the sum of the first 200 positive integers.
a1=23 d=-2

Answer 1

I have to find a200 right? a200=23 + (200-1)-2

right? is this correct?

Answer 2

Key words, "Sum" and "Positive" terms.

Answer 3

Sum meaning the addition of all terms found using the formula, positive terms only.

Answer 4

Sum formula:
\[S_n = \frac{ n(a_1-a_n) }{ 2 }\]

Where
Sn = the sum of the n terms.
a1 = the first term
an = the nth term

Answer 5

You seem to have everything except for an which you know how to find.

Answer 6

so \[S _{200}= 200(23-a _{n})/\]

Answer 7

Correct.

Answer 8

over 2

Answer 9

I have to find an

Answer 10

\[a _{200}\]

Answer 11

You can use the formula for the Nth term:\[a_n = a_1+(n-1)d\]

Answer 12

Correct

Answer 13

\[a _{200}= 23 + (200-1)-2\]

Answer 14

The formula should be

\[\Large S_n = \frac{ n(a_{1}+a_{n}) }{ 2 }\]

notice how It's "a1 + an" and not "a1 - an"

Answer 15

Yes, but I need to find an first

Answer 16

I get \[a _{200} = -375\]

Answer 17

You want the sum of the first 200 terms

so plug in n = 200 into the Sn sum formula

\[\Large S_n = \frac{ n(a_{1}+a_{n}) }{ 2 }\]

\[\Large S_{200} = \frac{ 200(a_{1}+a_{200}) }{ 2 }\]

do you see where to go from here?

Answer 18

is a200= -375 ?

Answer 19

correct

Answer 20

I get -35200

Answer 21

me too

\[\Large S_{200} = -35200\]

Answer 22

in the answer key it says it is 20,100

Answer 23

The problem is

"Find the sum of the first 200 positive integers. a1=23 d=-2"

right?

Answer 24

Are you sure d = -2?

Answer 25

well, a1= 23 d=-2 is from the previous question, I assumed the question was referring to that

Answer 26

oh so you want to add up 1, 2, 3, ..., 198, 199, 200 ???

Answer 27

if so, then

a1 = 1
a200 = 200
n = 200

Answer 28

ohhh

Answer 29

my fault D:

Answer 30

thanks

Answer 31

no worries and yw