Question

If Mean of the terms a, a+3, a+6, a+9 and a+12 is 10, then a is equal to;

Answer 1

$Given \:mean \: of \: the \: data :$

$a, a+3,a+6,a+9 \:and \: a+12\: is \: 10$

$\boxed{ \pink{ Mean = \frac{sum \: of \: the \: terms }{Number \: of \: terms }}}$

$Mean = 10$

$\implies \frac{ a+a+3+a+6+a+9+a+12}{5} = 10$

$\implies \frac{5a + 30}{5} = 10$

$\implies \frac{5(a + 6)}{5} = 10$

$\implies a + 6 = 10$

$\implies a = 10 - 6$

$\implies a = 4$

Therefore.,

$\red{ Value \:of \: a }\green { = 4 }$

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Answer 2

Given :

• Mean of 5 terms ( a, a+3, a+6, a+9 and a+12) = 10

To find :

• value of a

Formula used :

$mean = \dfrac{sum \: of \: terms}{number \: of \: terms}$

Solution :

Sum of terms = a+a+3+a+6+a+9 + a+12

Sum of terms = 5a+30

Number of terms = 5

Mean = 10

Now According to the question :-

$\implies10 = \dfrac{5a + 30}{5}$

Now cross multiply.

$\implies50 = 5a + 30$

$\implies50 - 30 = 5a$

$\implies20 = 5a$

$\implies \dfrac{20}{5} = a$

$\implies4= a$

Answer :

value of a = 4

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Verification of Answer :-

We can verify our answer by first finding out 5 terms :-

⟹ 4, 4+3, 4+6, 4+9 and 4+12

⟹ 4 , 7 , 10 , 13 , 16

Now find mean of 4 , 7 , 10 , 13 , 16. If we get mean as 10 then the answer is correct.

⟹ Mean = (4 + 7 +10 + 13 +16)/5

⟹ Mean = 50 / 5

⟹ Mean = 10

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