Question

HELP!!!!!
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true.

Sn: 1^2 + 4^2 + 7^2 + . . . + (3n - 2)^2 = n(6n^2-3n-1)/2

Answer 1

CAN YOU HELP ME...MY OLDER BRO MAKES ME DO HIS WORK SO I HAVE NO CLUE WHAT IM DOING

Answer 2

for S1 just plug n = 1 into the formula and see if it works out to 1^2 ( 1)

Answer 3

S1 = 1(6*1^2 - 3(1) - 1) / 2

Answer 4

what does that work out to?

Answer 5

that work out for S2, and S3 too. just plug n =2, and n =3 into the equation, you can see that it works for both them.

Answer 6

17.5 ?

Answer 7

how did you get thatt?

Answer 8

1(6*1^2 - 3(1) - 1) / 2 I DID THIS

Answer 9

ok
that 1 * (6 - 3 -1) / 2

work out the brackets first

= 1 * 2 / 2
= 2 / 2
= 1

which checks out

Answer 10

follow?

Answer 11

YES

Answer 12

ok so do the same thing for S2 ( n = 2)
and the result
should equal the sum of 2 terms
- that -s 1^2 + 4^2 which is 1 + 16 = 17

Answer 13

SO WHAT WILL THE ANSWER BE @cwrw238 IM CONFUSED

Answer 14

plug in n = 2 into the formula

Sn = n (6n^2 - 3n - 1) / 2

so

S2 = 2(6*2^2 - 3*2 - 1 ) / 2

you just replace every n in the formula by 2 and work it out

do brackets first

what is 6* 2^2 - 3*2 - 1 equal to?

Answer 15

17

Answer 16

do you know what the symbols mean
what is 2^2 /

Answer 17

right 17

Answer 18

DIVIDE

Answer 19

so we have 2 * 17 / 2

Answer 20

17

Answer 21

= 34 / 2 = 17

thats the answer we require

because S2 (th sum of the first 2 terms) = 1^2 + 4^2 = 17

Answer 22

OK SO THEN WHAT YOU DID

Answer 23

yes
work out the sum from the formula the
check it against the sum you get by adding the number of terms

so for S3 plug s=3 into the formula
and that should work out to 1^2 + 4^2 + 7^2 = 1 + 16 + 49 = 66

if it does then the statement is true

Answer 24

WHAT DO I SUM UP AGAIN?

Answer 25

17 +17 +66?

Answer 26

no S3 means the sum of the first 3 terms

that is 1^1 ^ 4^2 + 7^2 = 1 + 16 + 49 which equlas 66

Answer 27

OH SO THE WHOLE ANSWER IS 66 @cwrw238 IM GOING TO THE 6TH GRADE SO I DONT KNOW WHAT THE HECK IM DOING

Answer 28

yes - now if you plug in n= 3 into the formula and work it out you should get 66
- this proves that he formula is true for S3.

Answer 29

SO IS THIS WHAT MY ANSWER SHOULD LOOK LIKE

S1 = 1(6*1^2 - 3(1) - 1) / 2=17
S2 = 1^2 + 4^2 = 17
S3 = 1^2 + 4^2 + 7^2 = 66

@cwrw238

Answer 30

S2 and S3 are correct but S1 = 1

Answer 31

oh okay

Answer 32

S1 = 1(6*1^2 - 3(1) - 1) / 2=1
S2 = 1^2 + 4^2 = 17
S3 = 1^2 + 4^2 + 7^2 = 66

Answer 33

yea

Answer 34

thank you so much @cwrw238

Answer 35

thats ok