Question

If x-1 , x +3,3 x-1 are in A.P, then the value of x is
a) 4
B)-4
c) 2
d)-2​

Answer 1

GIVEN :–

• x - 1 , x + 3 , 3x - 1 are in A.P.

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

• If three terms a , b , c are in A.P. then relation between them –

$\\ \longrightarrow \large{ \boxed{ \bold{b = \dfrac{a + c}{2} }}}$

• Here –

$\\ \: \: \: \:{ \huge{.}} { \bold{ \: \: a = x - 1 }}$

$\\ \: \: \: \:{ \huge{.}} { \bold{ \: \: b = x + 3 }}$

$\\ \: \: \: \:{ \huge{.}} { \bold{ \: \: c = 3x - 1 }}$

• So that –

$\\ \implies { \bold{x + 3 = \dfrac{(x - 1) +(3x - 1)}{2} }}$

$\\ \implies { \bold{x + 3 = \dfrac{x + 3x-2}{2} }}$

$\\ \implies { \bold{x + 3 = \dfrac{4x-2}{2} }}$

$\\ \implies { \bold{x + 3 = 2x -1}}$

$\\ \implies { \bold{ 3+1 = 2x - x }}$

$\\ \longrightarrow \large{ \boxed{ \bold{x= 4 }}}$

• Hence, Option (a) is correct.

Answer 2

✯✯ QUESTION ✯✯

If x-1 , x+3 , 3x - 1 are in A.P, then the value of x is :

A) 4

B) -4

C) 2

D) -2

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt\bold{x-1 , x+3 , 3x-1}$

➥Now ,

➥Using Formula :

$\longmapsto\tt{\large{\boxed{\bold{\bold{\blue{\sf{b=\dfrac{a+c}{2}}}}}}}}$

➥Here :

• a = x - 1
• b = x + 3
• c = 3x - 1

➥Putting Values : -

$\longmapsto\tt{\dfrac{x+3}{1}=\dfrac{x-1+3x-1}{2}}$

$\longmapsto\tt{2(x+3)=1(x-1+3x-1)}$

$\longmapsto\tt{2x+6=x-1+3x-1}$

$\longmapsto\tt{2x-x-3x=-1-1-6}$

$\longmapsto\tt{1x-3x=-2-6}$

$\longmapsto\tt{-2x=-8}$

$\longmapsto\tt{\cancel\dfrac{-8}{-2}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{k}\orange{=}\purple{4}}}$

☛So , The value of k is 2 and option a) is correct..