What is the average of all the numbers between 7 and 56 that are divis

1.	What is the average of all the numbers between 7 and 56 that are divisible by 6?1. 37.52. 333. 364. 30
Answer» Correct Answer - Option 2 : 33 Given: the average of all the numbers between 7 and 56 that are divisible by 6 Concept used: Average Calculation: Numbers between 7 and 56 divisible by 6 ⇒ 12,18,24....54 All these numbers are in Arithmetic progression. Common difference (d) = 6 Average of terms of AP = \(\frac{{\left( {a + l} \right)}}{2}\) a is the first term and l is the last term. Average : \(\frac{{12\ +\ 54}}{2} = 33\) Second method: Between 7 and 56 numbers which are divisible by 6 ⇒ 12,18,24...54 Common difference (d) = 6 Number of terms = \(\frac{{\left( {{\rm{Last\ term - First \ term}}} \right)}}{{{\rm{common \ difference}}}} + 1\) Number of terms = \(\frac{{\left( {54 - 12} \right)}}{6} + 1\) Number of terms (N) = 8 Sum of N terms = \(\frac{n}{2}\left( {a + l} \right)\) Sum = 4 × (12 + 54) Sum = 264 Average = Sum / Total number of terms Average = \(\frac{{264}}{8}\) Average = 33

What is the average of all the numbers between 7 and 56 that are divisible by 6?1. 37.52. 333. 364. 30

Answer» Correct Answer - Option 2 : 33

Given:

the average of all the numbers between 7 and 56 that are divisible by 6

Concept used:

Average

Calculation:

Numbers between 7 and 56 divisible by 6

⇒ 12,18,24....54

All these numbers are in Arithmetic progression.

Common difference (d) = 6

Average of terms of AP = \(\frac{{\left( {a + l} \right)}}{2}\)

a is the first term and l is the last term.

Average : \(\frac{{12\ +\ 54}}{2} = 33\)

Second method:

Between 7 and 56 numbers which are divisible by 6

⇒ 12,18,24...54

Common difference (d) = 6

Number of terms = \(\frac{{\left( {{\rm{Last\ term - First \ term}}} \right)}}{{{\rm{common \ difference}}}} + 1\)

Number of terms = \(\frac{{\left( {54 - 12} \right)}}{6} + 1\)

Number of terms (N) = 8

Sum of N terms = \(\frac{n}{2}\left( {a + l} \right)\)

Sum = 4 × (12 + 54)

Sum = 264

Average = Sum / Total number of terms

Average = \(\frac{{264}}{8}\)

Average = 33