Question

Last ones I need help with!

Answer 1

so the common difference =d= +2

a1 = January clients = 5

use the formula \(\Large a_n = a_1 +(n-1)d\)

Answer 2

december means n = 12

Answer 3

Alright so
a_n=a_1(n-1)d
a_n=5+(n-1)2
a_n=5+(12-1)2
a_n=5+11(2)
a_n=5+22
a_n=27

Answer 4

correct, 27 clients in december

Answer 5

to get the total number of clients in 12 months, we need to add all the clients she added each month!

we could use this sum formula
\(\Large S_n = (n/2) (2a+(n-1)d)\)
n = 12

Answer 6

that \(a\) is actually \(a_1\)

Answer 7

S_n=(n/2)(2a_1+(n-1)d)
S_n=(12/2)(2(5)+(12-1)2)
S_n=(6)(10+(11)2)
S_n=(6)(10 + 22)
S_n=(6)(32)
S_n=192

Answer 8

correct :)
ask if any doubts...

Answer 9

Hahaa.
Okay great so I don't know how to do the sigma ones at all.

Answer 10

\(\Large \sum = sum\)

\(\sum \limits_{n=1}^6\)
means sum from 1st term to 6th term

Answer 11

one easier approach to do both 2 and 3, (just because the upper limit is small)
is to keep on plugging in numbers for n

plug in n =1, then n=2, then n=3....n=6 and add all the answers

Answer 12

for 3.
start with n = 0, go till n =5
add all the answers

Answer 13

So for 2
n^2+1
1^2+1=1+1=2
2^2+1=4+1=5
3^2+1=9+1=10
4^2+1=16+1=17
5^2+1=25+1=26
6^2+1=36+1=37
2+5+10+17+26+37=97

Answer 14

too lazy to check, i assume thats correct :P

Answer 15

yup, 97 is correct

Answer 16

Lol okay
For 3
16(1/4)^n
16(1/4)^0=16*1=16
16(1/4)^1=16*.25=4
16(1/4)^2=16*.0625=1
16(1/4)^3=16*.015625=.25
16(1/4)^4=16*.00390625=.0625
16(1/4)^5=16*9.765625E-4=.015625
16+4+1+.25+.0625+.015625=21.328125

Answer 17

correct! :)

Answer 18

Ok so how do I determine the last one.

Answer 19

can you find the common ratio between the terms of the last sequence ?

Answer 20

if magnitude of common ratio |r| > 1 , then the series does not converge at all and the sum would be infinite

Answer 21

So to find r
Do I do it like this?
1/4 to 1/2 or is it 1/4 to -1/2?

Answer 22

r = 2nd term / 1st term = 3rd term/ 2nd term = ...

Answer 23

-1/2 divided by 1/4

or simply -2 divided by 1

Answer 24

-1/2 divided by 1/4 =
-2
-2 divided by 1=
-2
|r|>1
|-2|>1
2>1

Answer 25

correct, so the sum does not even exist, as the sequence is divergent

Answer 26

Alright thank you!

Answer 27

welcome ^_^