Question

If the second, third and fourth terms of a proportion are 3,4 and 6 respectively, find the first

term​

Answer 1

Solution:-

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$\large\to{\underbrace{\underline{\sf{Understanding\:the\:concept:-}}}}$

$\green \implies$ Here it is given in the question that the second, third and fourth terms of a proportion are 3, 4 and 6 respectively. Now the question has asked us to find out the 1st term.

⛥ HOW TO DO:-

$\green \implies$ To find the 1st term of proportion we need to apply the formula of product of means and product of extremes. So first we have to form an equation by assuming the 1st term as x and then solve it. Follow the steps below to get the answer.

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ANSWER:-

❍ The first term is 2.

GIVEN:-

➡ 2nd term = 3

➡ 3rd term = 4

➡ 4th term = 6

TO FIND:-

• Here we have to find the 1st term of proportion.

SOLUTION:-

• As mentioned above we have to use the formula of product of means and product of extremes.
• Let the 1st term be x.

We know that:-

$\underline{\boxed{\purple \bigstar \pmb {\red{Product \: of \: means = Product \: of \: extremes}}}}$

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So, let's solve it!

• Finding the 1st terms:-

$\dashrightarrow \tt {\underbrace {x : {\underbrace{3 :: 4}} : 6}}$

$\dashrightarrow \tt{Product \: of \: means = 3 \times 4}$

$\dashrightarrow \tt{Product \: of \: extremes = x \times 6}$

$\dashrightarrow \tt{3 \times 4 = x \times 6}$

$\dashrightarrow \tt{12 = 6x}$

$\dashrightarrow \tt{Transposing \: 6 \: to \: L.H.S.}$

$\dashrightarrow \tt{ \dfrac{12}{6} = x}$

$\dashrightarrow \tt{ \dfrac{ \not1 \!\!\!\not2}{ \not6} = x}$

$\dashrightarrow \tt{ \dfrac{2}{1} = x}$

$\overline{\boxed{ \purple \odot \: \blue{ 2 = x}}}$

Thus, the 1st term is 2.

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