Question

$\huge\underline{\overline{\mid{\bold{\purple{\mathcal{Question:-}}\mid}}}}$

⟹ The sum of three terms in an A.P. is 21 and their product is 231. Find the numbers.

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Kindly:-

⇝ Do explain properly

why to take a, a-d and a+d instead of a, a+d and a+2d.

∙⇝ Quality answer required! ​

Answer 1

Ur Answer:-

Let the required numbers be (a - d), a, (a +d).

Then,

a- d +a+a+d= 21

3a = 21

a=7

Also,

(a-d)a(a+d) = 231

a(a - d3) = 231

7(49 d3) = 231

7d= 112

d2= 16

d= t4

Hence, the required numbers are (3, 7,11) or

(3, 7,11) or(11,7,3).

Answer 2

$\huge\underline{\overline{\mid{\bold{\purple{\mathcal{Question:-}}\mid}}}}$

⇒ The sum of three terms in an A.P. is 21 and their product is 231. Find the numbers.

Given:-

• The sum of 3 numbers in A.P is 21 and the product is 231.

To find:-

• The 3 numbers

$\huge\underline{\overline{\mid{\bold{\purple{\mathrm{Solution:- }}\mid}}}}$

Let the first term be a, and the common difference be d (as it is an arithmetic progression)

$\underline{ \boxed{ \sf \: Let \: (a-d),a,(a+d) \: are \: 3 \: numbers \: in \: A.P}}$

Let(a−d),a,(a+d)are3numbersinA.P

$\blue{ ⇒a - d + a + a + d = 21}$

$\pink{⇒3a = 21}$

$\blue{➦a = \frac{21}{3}}$

$\pink{➦a = 7}$

$\blue \implies \: (a - d)a(a + d) = 231$

$\pink \implies \: a( {a}^{2} - {d}^{2} ) = 231$

$\blue\implies \: 7(49 - {d}^{2} ) = 231$

$\pink\implies49 - {d}^{2} = \frac{231}{7}$

$\blue\implies49 - {d}^{2} = 33$

$\pink\implies{d}^{2} = 49 - 33$

$\blue\implies{d}^{2} = 16$

$\pink\implies \: d = \sqrt{16}$

$\blue\implies \: d = 4$

⇰a-d =7-4=3

⇰a+d=7+4=11

⇰a=7

$\boxed{ \underline{ \mathcal{ \green{Therefore \: the \: numbers \: are \: 3,11,7}}}}$

Thereforethenumbersare3,11,7