Question

If Mean of a, a+3, a+6, a+9 and a+12 is 10, then a is equal to;
A). 1
B). 2
C). 3
D). 4​

Answer 1

Answer:

Question

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

To find

value of a

Solution

${ \underline { \boxed{\sf{Mean = \frac{sum \: of \: the \: terms}{no.of \: terms} }}}}$

$\sf{ \to \: sum \: of \: the \: terms = a + (a + 3) + (a + 6 )+( a + 9 )+ (a + 12)} \\ \\ \sf{ \to \: no.of \: terms = 5}$

Subsitute the values in the mean formula:-

$\sf{ \to \: mean = \frac{5a + 30}{5} } \\ \\ \sf{ \to \: 10 = \frac{5a + 30}{5} } \\ \\ \sf{ \to \: 50 = 5a + 30} \\ \\ \sf {\to \: 20 = 5a} \\ \\ \sf{ \to \: a = \frac{20}{5} } \\ \\ \sf{ \to \: a= 4}$

$\sf{ \underline{ \therefore \: the \: correct \: option \: is \: d)4.}}$

_________________________

Answer 2

$\huge\mathtt{\fbox{\red{Answer}}}$

$\large{\boxed{\bf{ \star\:\: d).4.\:\: \star}}}$

To find

value of A

Solution

${ \underline { \boxed{\sf{\red{Mean = \frac{sum \: of \: the \: terms}{no.of \: terms} }}}}}$

$\sf{ \to \: sum \: of \: the \: terms = a + (a + 3) + (a + 6 )+( a + 9 )+ (a + 12)} \\ \\ \sf{ \to \: no.of \: terms = 5}$

Subsitute the values in the mean formula:-

$\sf{ \to \: mean = \frac{5a + 30}{5} } \\ \\ \sf{ \to \: 10 = \frac{5a + 30}{5} } \\ \\ \sf{ \to \: 50 = 5a + 30} \\ \\ \sf {\to \: 20 = 5a} \\ \\ \sf{ \to \: a = \frac{20}{5} } \\ \\ \sf{ \to \: a= 4}$

$\sf{ \underline{ \therefore \: the \: correct \: option \: is \: d)4.}}$