Question

For an AP, the sum of the first 100 and the sum of the first 10 terms are 10 and 100 respectively. What is the sum of the first 110 terms of the AP.

Answer 1

@wio a easy one

Answer 2

Hmmm, yeah, it's not too hard. Do you need help?

Answer 3

ye just show me the method lol

Answer 4

i keep getting the wrong answer

Answer 5

First, do you know the formula for an AP?

Answer 6

\[
a_n = a_1+(n-1)d
\]

Answer 7

\[
S_n=\frac{n}{2}\left(\frac{a_1+a_n}{2}\right)
\]

Answer 8

ye i know

Answer 9

Combine to get: \[
\frac{n}{2}\left(\frac{2a_1+(n-1)d}{2}\right)
\]

Answer 10

Plugging in \(n\) and \(S_n\) will give you two formulas, which you can use to solve for \(a_1\) and \(d\).

Answer 11

what is your answer

Answer 12

No, I refuse to give you the answer. I have given you the means to solve it.

Answer 13

i cant get the right answer, mine has heaps of fractions

Answer 14

When \(n=100\), \(S_n=10\)

Answer 15

So\[
\frac{100}{2}\left(\frac{2a_1+(100-1)d}{2}\right) = 10
\]

Answer 16

When \(n=10\), \(S_n=100\).

Answer 17

So\[
\frac{10}{2}\left(\frac{2a_1+(10-1)d}{2}\right) = 100
\]

Answer 18

is d -11/25

Answer 19

my answer is -2310

Answer 20

the options are 90, -90, 110, -110, 100

Answer 21

@wio help

Answer 22

the first thing you need to do is to fix wio's formula. it is a little off

Answer 23

Whoops, I divided by two twice.

Answer 24

yea thats why

Answer 25

"what is your answer?" laughing out loud

Answer 26

k if u could help me, that would be greatly appreciated

Answer 27

\[S_n = \frac{n}{2}(2a_1 + (n-1)d)\]

\[S_{100} = 10 \implies 50(2a_1 + 99d)=10\tag{1}\]
\[S_{10} = 100\implies 5(2a_1+9d) = 100\tag{2}\]

two equations and two unknowns, you can solve them

Answer 28

i got 0/..........

Answer 29

@ganeshie8 i still can't get it please help me

Answer 30

can u check that d = -1/5 and a1 = 10.9

Answer 31

the idea is to fist solve \(a_1\) and \(d\), then use thes to find S_100

Answer 32

but mine is still wrong

Answer 33

Ohk you have already solved a and d

Answer 34

but my answer is 0.
it is multiple choice and the options are 90, -90, 110, -110, -100

Answer 35

yeah it looks messy, wish there is a better method

Answer 36

did u get 0 as well?

Answer 37

http://www.wolframalpha.com/input/?i=solve+50%282a_1%2B99d%29%3D10%2C+5%282a_1%2B9d%29%3D100

Answer 38

a1 = 10.99
d = -0.22

Answer 39

use them

Answer 40

-110...

Answer 41

i must be really bad but thanks both of u