Question

I need to find the four arithmetic means between -21 and -36

Answer 1

\(\large\color{darkblue}{ \rm -21,~~\text{_},~~\text{_},~~\text{_},~~\text{_},~~36. }\)

\(\large\color{darkblue}{ \rm -21+5d=-36. }\)
\(\large\color{darkblue}{ \rm 5d=-15. }\)
\(\large\color{darkblue}{ \rm d=-3. }\)

\(\large\color{darkblue}{ \rm 21,\color{red} { ~-24,~-27,~-30,~-33,} ~-36 }\)

Answer 2

:O THANKYOUU! pleaseee help me with another onee!!

Answer 3

I need to find the four arithmetic means between 100 and 135

Answer 4

can you try it based on the previous problem ?

Answer 5

100+5d=135?

Answer 6

100, ` ___ ` ` ___ ` ` ___ ` ` ___ ` 135

yes... !

Answer 7

Find the d

Answer 8

(d is the difference btw the terms )

Answer 9

`100+5d=135 `
1) subtract 100 from both sides
2) divide both sides by 5

Answer 10

5d=35?

Answer 11

yes and divide both sides by 5 ?

Answer 12

d = ?

Answer 13

d=7?

Answer 14

So can you fill in the blanks ?

100, `___` `___` `___` ___` 135

Answer 15

107,114,121,128?

Answer 16

Yeeeah !!

Answer 17

THANKYOUUUU so muchh!

Answer 18

So when you have N arithmetic means between A and B

you say A+Nd=C
and solve for d,
knowing the number of means N
and knowing the number A and B

makes sense ?

Answer 19

it does thankyou soo much! would you help me with one more? please:)?

Answer 20

Sure :)

Answer 21

What is the 20th term of the following arithmetic sequence?
1/2, 1, 3/2, 2

Answer 22

1 - 1/2 = ? (this would be the difference - what you add to each term, to obtain the next term. )

(for the beginning )

Answer 23

So ` d = ½ `

Answer 24

ok :)?

Answer 25

now use the formula,

\(\large\color{darkblue}{ \rm a_1+d(n-1)=a_n }\)

In your case, \(\large\color{darkblue}{ \rm \frac{1}{2}+ \frac{1}{2}(20-1)=a_{20} }\) Makes sense ?

Answer 26

yes totally! so..

Answer 27

Can you find the \(\large\color{black}{ \rm a_{20} }\) ?

Answer 28

½ + ½(20-1) = A 20
½ + ½(19) = A 20
½(1) + ½(19) = A 20
½(20) = A 20
10=A 20

Answer 29

1(19)=a20?

Answer 30

See how I am getting A20 ?

Answer 31

I see now, ok I think I got it!

Answer 32

THANKYOUUUU!!!! :)

Answer 33

Anytime :)