Question

If x+1, 3x and 4x+2 are in ap find the value of x.

Answer 1

Answer:

$\large{\underline{\boxed{\sf x = 3}}}$

Step-by-step explanation:

Given that;

(x + 1), 3x , (4x + 2) ..... are in A.P.

So, their common difference must be same. Here, terms are -

• a₁ = x + 1
• a₂ = 3x
• a₃ = 4x + 2

According to the question ;

a₂ - a₁ = a₃ - a₂

⇒ 3x - (x + 1) = 4x + 2 - 3x

⇒ 3x - x - 1 = x + 2

⇒ 2x - 1 - x = 2

⇒ x = 2 + 1

⇒ x = 3

Hence, the value of x is 3.

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The required A.P is ;

• a₁ = x + 1 = 3 + 1 = 4
• a₂ = 3x = 3 * 3 = 9
• a₃ = 4x + 2 = 4*3 + 2 = 14

Hence, the common difference is 5.

Answer 2

Answer:

$\huge{\red{\boxed{\green{\sf{x=3}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: \: {\pink{given}} \\ { \therefore{\green {\boxed{A.P= x + 1,3x,4x + 2}}}} \\ {\therefore \green {\boxed{a1 = x + 1}}} \\ {\therefore \green {\boxed{d = 3x - x - 1 = 2x - 1}}} \\ \\ {\blue{to \: find}} \\ {\red {\boxed{x =? }}}$

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$\to according \: to \: given \: information \: \\ \to we \: can \: find \: the \: value \: of \: x \\ \to so \: we \: know \: that \: in \: an \: ap \\ \to 2b = a + c \\ \\ putting \: the \: values \: of \: a \: b \: and \: c \\ \to 2(3x) = x + 1 + 4x + 2 \\ \to 6x = 5x + 3 \\ \to 6x - 5x = 3 \\ \to \: x = 3$

$\huge{\red{\boxed{\green{\sf{x=3}}}}}$

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