Average Test-2 (Finding average of specified numbers)

Answer: Option D

Explanation

According to the formula,

The average of first 'n' natural numbers

$=\left(\frac{\mathrm{n}+1}{2}\right)$

Here,

  n=101

∴ Required average$=\frac{101+1}{2}=\frac{102}{2}$

= 51

Hence, Option D is correct.

Answer: Option C

Explanation

According to the formula,

The average of 'n' multiples of a number =$\frac{\mathrm{Number}\times \left(\mathrm{n}+1\right)}{2}$

∴ n=80, number=4

∴ Required average =$\frac{4\times \left(80+1\right)}{2}=\frac{324}{2}=162$

Hence, Option C is correct.

Answer: Option A

Explanation

According to the formula,

The average of 'n' multiples of a number =$\frac{\mathrm{Number}\times \left(\mathrm{n}+1\right)}{2}$

∴ n=100, number=2

∴ Required average =$\frac{2\times \left(100+1\right)}{2}=\frac{202}{2}=101$

Hence, Option A is correct.

Answer: Option B

Explanation

According to the formula,

The average of squares of first 'n' natural numbers =$\frac{(n+1)(n+2)}{6}$

Here, n=50

∴ Required average 

$$\begin{gathered} =\frac{\left(50+1\right)\left(2\times 50+1\right)}{6} \\ =\frac{51\times 101}{6} \\ =\frac{5151}{6}= 858.5 \end{gathered}$$

Hence, Option B is correct.

Answer: Option A

Explanation

Given averages 2, 5, 8, 11, 14, 17…..41, 44, 47, 50.

The difference between any two numbers written in continuos sequence is 3.

we know the formula

The average of consecutive number =$\frac{\mathrm{First} \mathrm{number}+\mathrm{Last} \mathrm{number}}{2}$

Here,

First number= 2 and Last number =50

∴ Required average

$$\begin{gathered} =\frac{2+50}{2} \\ =\frac{52}{2} \\ =26 \end{gathered}$$

Hence, Option A is correct.