Question

If the mean of \[x,(x + 2),(x + 4),(x + 6),(x + 8)\] is 20 then x is
A) 32
B) 16
C) 8
D) 4

Answer 1

Hint: Mean is the average of the observations that have been provided. We will apply the simple method of the mean formula of individual series. To calculate the mean the formula is \[{\text{Mean}} = \dfrac{{{\text{Sum of observations}}}}{{{\text{No}}{\text{. of observations}}}}\]. We have been given the observations in terms of x and by counting the observations we can easily get the number.

Complete step-by-step solution:
We know the formula of mean as,
\[{\text{Mean}} = \dfrac{{{\text{Sum of observations}}}}{{{\text{No}}{\text{. of observations}}}}\]
Already given,
Terms = \[x,(x + 2),(x + 4),(x + 6),(x + 8)\]
Mean = 20
No. of observations = 5
Now by substituting the given value in the above mean formula
\[ \Rightarrow 20 = \dfrac{{x + (x + 2) + (x + 4) + (x + 6) + (x + 8)}}{5}\]
By opening the brackets, we get
\[ \Rightarrow 20 = \dfrac{{x + x + x + x + x + 2 + 4 + 6 + 8}}{5}\]
Taking 5 on the LHS and simplifying the solution, we get
\[ \Rightarrow 20 \times 5 = 5x + 20\]
\[ \Rightarrow 100 = 5x + 20\]
By taking 20 on the other side, we get
\[ \Rightarrow 100 - 20 = 5x\]
\[ \Rightarrow 80 = 5x\]
Finally, by dividing 80 by 5, we get
\[ \Rightarrow x = \dfrac{{80}}{5}\]
\[ \Rightarrow x = 16\]
Hence, the required value of x is 16.
Therefore, the correct option is B
Since we have got the value of, thus we can also find the value of terms.
1st term \[ \Rightarrow x = 16\]
2nd term \[ \Rightarrow x + 2 = 16 + 2 = 18\]
3rd term \[ \Rightarrow x + 4 = 16 + 4 = 20\]
4th term \[ \Rightarrow x + 6 = 16 + 6 = 22\]
5th term \[ \Rightarrow x + 8 = 16 + 8 = 24\]

Note: We shall only use the simple mean of the individual series method. Since there is nothing given, any alternative formula will not give a result. We have reversed the mean formula, thus there may be situations where the observations are given, and the mean needs to be determined.