Question

The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?

Answer 1

the fourth number in the sequence is 35

Answer 2

Answer:

The fourth number in the sequence is 35.

Step-by-step explanation:

Given : The sum of 6 consecutive odd numbers is 204.

To find : What is the fourth number in this sequence?

Solution : Let x be the smallest odd number of the sequence

Then the consecutive numbers are x, x+2, x+4, x+6, x+8, x+10

The sum of the numbers are :

$x+ x+2+ x+4,+x+6+ x+8+ x+10= 6x+30$

We have given that sum of  6 consecutive odd numbers is 204.

So, equating both we get,

$6x+30=204$

$6x=204-30=174$

$x=\frac{174}{6}$

$x=29$

So, The first term is x= 29

Second term is x+2=29+2=31

Third term is x+4=29+4=33

Fourth term is x+6=29+6=35

Fifth term is x+8=29+8=37

Sixth term is x+10=29+10=39

Therefore, The fourth number in the sequence is 35.