Question

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 + 5 + 8 + . . . + ( 3n - 1) = n(1 + 3n)/2

Answer 1

@bibby

Answer 2

They give you the generic formula. plug in for n=1 n=2 and n=3

Answer 3

how do I do that?

Answer 4

manually. read \(S_1\) as the summation of the first term of the sequence.
for example S5=2+5+8+11+14=5(1+15)/2 =5(16)/2=40

Answer 5

\(S_5\) was defined as the first 5 terms added up. we could use a calculator or the formula. They're equivalent.

\( S_5=2+5+8+11+14=5(1+15)/2 =\frac{5(16)}{2}=40\)

Answer 6

Oh okay I think I get it now :p

Answer 7

s1:2+5+8+(3(1)-1)=1(1+3(1))/2 ?

Answer 8

@bibby

Answer 9

3n - 1 is the last term in the series
where n=1, 2 is our first and only term

n=2, 5, is the last one

n=3 8 is the last term

Answer 10

so \(S_1=2=\large \frac{ n(1 + 3n)}{2}=\frac{ 1(1 + 3(1))}{2}=\frac{ (1 + 3)}{2}=2\)

Answer 11

So that's the first one ? Now I have to find s2 and s3 ?

Answer 12

yeah

Answer 13

Is that first one suppose to be an N?

Answer 14

one as in 1?

Answer 15

Nvm , I don't get it now im confused again

Answer 16

what're you t yping?

Answer 17

Im not typing anything my laptop acts stupid lol

Answer 18

lol it's the site, not the laptop

Answer 19

\(S_n: 2 + 5 + 8 + . . . + ( 3n - 1) = \large \frac{n(1 + 3n)}{2}\)
\(S_1: 2 + 5 + 8 + . . . + ( 3(1) - 1) = (3-1)=2=\large \frac{(1)(1 + 3(1))}{2}=\frac{4}{2}=2\)
\(S_2: 2 + 5 + 8 + . . . + ( 3(2) - 1) = (6-1)=5=2+5=7=\large \frac{(2)(1 + 3(2))}{2}=\frac{14}{2}=7\)

Answer 20

7 ?

Answer 21

yeah, it got cut off lol

Answer 22

Oh okay lol , what about s3 ?

Answer 23

the sum of the first 3 terms

Answer 24

or 3(1+3(3))/2
=3(10)/2=15

Answer 25

2+5+8=15

Answer 26

\[S3:2+5+8+...+(3(3)-1)=9-1=8=\]

Answer 27

so what is 2+5+8

Answer 28

that whole 3(3)-1 is just the last term in the series

Answer 29

\(S_3=2+5+8+...+(3(3)-1)\) that means 8 is the last term in this sum
\(S_3=2+5+8=\frac{3(3(3)+1)}{2}=\frac{30}{2}=15\)