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.

Sn: 2 + 5 + 8 + . . . + ( 3n - 1) = n(1 + 3n)/2

Answer 1

u knw what S1 means ?

Answer 2

S1 means this :-
sum of first 1 terms

Answer 3

S2 means, sum of first 2 terms
S3 means, sum of first 3 terms

.........
S1000 means, sum of first 1000 terms

Answer 4

we're given the series formula :-

Sn = 2 + 5 + 8 + ....... + (3n+1) = n(1+3n)/2

Answer 5

use this, and can u calculate S1 ?

Answer 6

Sn = n(1+3n)/2
S1 = 1(1+3*1)/2
= ?

Answer 7

well S1 = 2?

Answer 8

sorry @ganeshie8 had to grab some to munch on lol

Answer 9

yup ! thats the sum of first 1 terms

Answer 10

ohk... np :)

Answer 11

now find sum of first 1 terms manually

Answer 12

what you mean by that

Answer 13

first term is 2 itself, so yes the Sn formula is correct for S1

Answer 14

2 + 5 + 8 + ....... + (3n+1)
^

Answer 15

Next, find S2 using the formula

Answer 16

Sn = n(1+3n)/2
S2 = ?

Answer 17

what do i plug in for n?

Answer 18

2

Answer 19

so S2 = 7

Answer 20

yup, now add the first two numbers in given sequence manually and see wat u get

Answer 21

2 + 5 + 8 + ....... + (3n+1)
^ ^

Answer 22

7!

Answer 23

so... S2 is true

Answer 24

next, find S3 using the formula

Answer 25

Sn = n(1+3n)/2
S3 = ?

Answer 26

15

Answer 27

now as usual, add the first 3 terms manually and see wat u get

Answer 28

15

Answer 29

So its same, so the formula is verified for S1, S2, S3

Answer 30

okay got it (:

Answer 31

cool :) also observe the general term :-

Sn = 2 + 5 + 8 + ....... + (3n+1) = n(1+3n)/2
^^^^^

we could have found the first few terms using that general term as well :-
general term an = 3n-1
so,
first term a1 = 3*1-1 = 2
second term a1 = 3*2-1 = 5
third term a3 = 3*3-1 = 8
...

Answer 32

oh okay gotchaa (: