If the average of 6 consecutive odd number is 42 find the sum of next set of 6 numbers
Answers
Answer:
Required six consecutive odd numbers are 37 , 39 , 41 , 43 , 45 and 47.
Step-by-step explanation:
Given,
Average of 6 consecutive odd numbers is 42.
Average of 6 number( as per demand ) = ( sum of 6 numbers ) / 6
42 = ( sum of 6 numbers ) / 6
42 x 6 = sum of 6 numbers
252 = sum of 6 numbers
Now, sum of six consecutive numbers is 252.
Let the required consecutive odd numbers are 2a + 1 , 2a + 3 , 2a + 5 , 2a
+ 7 , 2a + 9 , 2a + 11 .
According to the question:
= > sum of all the numbers = 252
= > ( 2a + 1 ) + ( 2a + 3 ) + ( 2a + 5 ) + ( 2a + 7 ) + ( 2a + 9 ) + ( 2a + 11 ) = 252
= > 2a + 1 + 2a + 3 + 2a + 5 + 2a + 7 + 2a+ 9 + 2a + 11 = 252
= > 2a + 2a + 2a + 2a + 2a + 2a + 1 + 3+ 5 + 7 + 9 + 11 = 252
= > 12a + 36 = 252
= > 12a = 252 - 36
= > 12a = 216
= > a = 216 / 12
= > a = 18
Therefore, required numbers are :
2a + 1 = 2( 18 ) + 1 = 36 + 1 = 37
2a + 3 = 2( 18 ) + 3 = 36 + 3 = 39
2a + 5 = 2( 18 ) + 5 = 36 + 5 = 41
2a + 7 = 2( 18 ) + 7 = 36 + 7 = 43
2a + 9 = 2( 18 ) + 9 = 36 + 9 = 45
2a + 11 = 2( 18 ) + 11 = 36 + 11 = 47
Answer :
The required numbers are 37 , 39 , 41 , 43 , 45 and 47.
Step - by - step explanation :
Average of six consecutive odd numbers is 42.
Average of six numbers = sum of 6 numbers / 6
⇒ 42 = sum of 6 numbers / 6
⇒ 42 × 6 = sum of 6 numbers.
⇒ 252 = sum of six numbers.
The sum of six numbers is 252.
Let the six consecutive odd numbers be x + 1, x + 3, x + 5 , x + 7 , x + 9 and x + 11.
According to question :
x + 1 + x + 3 + x + 5 + x + 7 + x + 9 + x + 11 = 252
⇒ 6x + 36 = 252
⇒ 6x = 252 - 36
⇒ 6x = 216
⇒ x = 216 / 6
⇒ x = 36
The required consecutive odd numbers are :
• ( x + 1 ) = 36 + 1 = 37
• ( x + 3 ) = 36 + 3 = 39
• ( x + 5 ) = 36 + 5 = 41
• ( x + 7 ) = 36 + 7 = 43
• ( x + 9 ) = 36 + 9 = 45
• ( x + 11 ) = 36 + 11 = 47
The six consecutive odd numbers are 37 , 39 , 41 , 43 , 45 and 47.